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A Geometric Embedding Approach to Multiple Games and Multiple Populations
Published 11 Jan 2024 in math.DS, cs.GT, and nlin.AO | (2401.05918v1)
Abstract: This paper studies a meta-simplex concept and geometric embedding framework for multi-population replicator dynamics. Central results are two embedding theorems which constitute a formal reduction of multi-population replicator dynamics to single-population ones. In conjunction with a robust mathematical formalism, this provides a toolset for analyzing complex multi-population models. Our framework provides a unifying perspective on different population dynamics in the literature which in particular enables to establish a formal link between multi-population and multi-game dynamics.
- Argasinski K (2006) Dynamic multipopulation and density dependent evolutionary games related to replicator dynamics. a metasimplex concept. Mathematical biosciences 202(1):88–114 Aström et al [2017] Aström F, Petra S, Schmitzer B, et al (2017) Image Labeling by Assignment. J Math Imag Vision 58(2):211–238 Ay et al [2017] Ay N, Jost J, Vân Lê H, et al (2017) Information Geometry, vol 64. Springer Baydin et al [2018] Baydin A, Pearlmutter B, Radul A, et al (2018) Automatic Differentiation in Machine Learning: a Survey. J Machine Learning Research 18:1–43 Bednar and Page [2007] Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Aström F, Petra S, Schmitzer B, et al (2017) Image Labeling by Assignment. J Math Imag Vision 58(2):211–238 Ay et al [2017] Ay N, Jost J, Vân Lê H, et al (2017) Information Geometry, vol 64. Springer Baydin et al [2018] Baydin A, Pearlmutter B, Radul A, et al (2018) Automatic Differentiation in Machine Learning: a Survey. J Machine Learning Research 18:1–43 Bednar and Page [2007] Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Ay N, Jost J, Vân Lê H, et al (2017) Information Geometry, vol 64. Springer Baydin et al [2018] Baydin A, Pearlmutter B, Radul A, et al (2018) Automatic Differentiation in Machine Learning: a Survey. J Machine Learning Research 18:1–43 Bednar and Page [2007] Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Baydin A, Pearlmutter B, Radul A, et al (2018) Automatic Differentiation in Machine Learning: a Survey. J Machine Learning Research 18:1–43 Bednar and Page [2007] Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. 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Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Ay N, Jost J, Vân Lê H, et al (2017) Information Geometry, vol 64. Springer Baydin et al [2018] Baydin A, Pearlmutter B, Radul A, et al (2018) Automatic Differentiation in Machine Learning: a Survey. J Machine Learning Research 18:1–43 Bednar and Page [2007] Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Baydin A, Pearlmutter B, Radul A, et al (2018) Automatic Differentiation in Machine Learning: a Survey. J Machine Learning Research 18:1–43 Bednar and Page [2007] Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Ay N, Jost J, Vân Lê H, et al (2017) Information Geometry, vol 64. Springer Baydin et al [2018] Baydin A, Pearlmutter B, Radul A, et al (2018) Automatic Differentiation in Machine Learning: a Survey. J Machine Learning Research 18:1–43 Bednar and Page [2007] Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Baydin A, Pearlmutter B, Radul A, et al (2018) Automatic Differentiation in Machine Learning: a Survey. J Machine Learning Research 18:1–43 Bednar and Page [2007] Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Baydin A, Pearlmutter B, Radul A, et al (2018) Automatic Differentiation in Machine Learning: a Survey. J Machine Learning Research 18:1–43 Bednar and Page [2007] Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bednar J, Page S (2007) Can game(s) theory explain culture?: The emergence of cultural behavior within multiple games. Rationality and Society 19(1):65–97. https://doi.org/10.1177/1043463107075108 Bengtsson and Zyczkowski [2017] Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. 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In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. 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Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Bengtsson I, Zyczkowski K (2017) Geometry of Quantum States: An Introduction to Quantum Entanglement, 2nd edn. Cambridge University Press Boll et al [2021] Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Boll B, Schwarz J, Schnörr C (2021) On the correspondence between replicator dynamics and assignment flows. In: Elmoataz A, Fadili J, Quéau Y, et al (eds) Scale Space and Variational Methods in Computer Vision. Springer International Publishing, Cham, pp 373–384 Bollacker et al [1998] Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Bollacker KD, Lawrence S, Giles CL (1998) Citeseer: An autonomous web agent for automatic retrieval and identification of interesting publications. In: Proceedings of the second international conference on Autonomous agents, pp 116–123 Bomze [1986] Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Bomze IM (1986) Non-cooperative two-person games in biology: A classification. International Journal of Game Theory 15(1):31–57 Chamberland and Cressman [2000] Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Chamberland M, Cressman R (2000) An example of dynamic (in)consistency in symmetric extensive form evolutionary games. Games and Economic Behavior 30(2):319–326 Chen [2013] Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Chen BY (2013) Segre embedding and related maps and immersions in differential geometry. URL http://arxiv.org/abs/1307.0459, 1307.0459[math] Cressman [1992] Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. 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In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. 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Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Cressman R (1992) The stability concept of evolutionary game theory: a dynamic approach, vol 94. Springer Cressman and Tao [2014] Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Cressman R, Tao Y (2014) The replicator equation and other game dynamics. Proceedings of the National Academy of Sciences 111(supplement_3):10810–10817 Drton et al [2009] Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. 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In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. 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Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Drton M, Sturmfels B, Sullivant S (2009) Lectures on Algebraic Statistics. Birkhäuser Basel, Basel Gardner [2003] Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Gardner RJ (2003) Games for business and economics, 2nd edn. Wiley, Hoboken, NJ Görtz and Wedhorn [2020] Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Görtz U, Wedhorn T (2020) Algebraic Geometry I: Schemes: With Examples and Exercises. Springer Studium Mathematik - Master, Springer Fachmedien, Wiesbaden Graham [1981] Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Graham A (1981) Kronecker Products and Matrix Calculus: with Applications. Ellis Horwood Limited Hamavar and Asl [2021] Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hamavar R, Asl BM (2021) Seizure onset detection based on detection of changes in brain activity quantified by evolutionary game theory model. Computer Methods and Programs in Biomedicine 199:105899 Hammerstein and Selten [1994] Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Hammerstein P, Selten R (1994) Game theory and evolutionary biology. In: Handbook of Game Theory with Economic Applications, vol 2. Elsevier, p 929–993 Harker and Pang [1990] Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48(1):161–220 Hashimoto [2006] Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Hashimoto K (2006) Unpredictability induced by unfocused games in evolutionary game dynamics. Journal of Theoretical Biology 241(3):669–675 Hofbauer [2001] Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J (2001) From nash and brown to maynard smith: Equilibria, dynamics and ess. Selection 1(1-3):81 – 88 Hofbauer and Sigmund [1998] Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge university press Hühnerbein et al [2020] Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Hühnerbein R, Savarino F, Petra S, et al (2020) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision Hühnerbein et al [2021] Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Hühnerbein R, Savarino F, Petra S, et al (2021) Learning Adaptive Regularization for Image Labeling Using Geometric Assignment. J Math Imaging Vision 63:186–215 Iacobelli et al [2016] Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Iacobelli G, Madeo D, Mocenni C (2016) Lumping evolutionary game dynamics on networks. Journal of Theoretical Biology 407:328–338 Jost [2017] Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Jost J (2017) Riemannian Geometry and Geometric Analysis, 7th edn. Springer Lee [2018] Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Lee JM (2018) Introduction to Riemannian Manifolds, vol 2. Springer Leimar and McNamara [2023] Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Leimar O, McNamara JM (2023) Game theory in biology: 50 years and onwards. Philosophical Transactions of the Royal Society B: Biological Sciences 378(1876):20210509 Madeo and Mocenni [2015] Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Madeo D, Mocenni C (2015) Game interactions and dynamics on networked populations. IEEE Transactions on Automatic Control 60(7):1801–1810 Madeo et al [2017] Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Talarico A, Pascual-Leone A, et al (2017) An evolutionary game theory model of spontaneous brain functioning. Scientific reports 7(1):1–11 Madeo et al [2020] Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Madeo D, Mazumdar S, Mocenni C, et al (2020) Evolutionary game for task mapping in resource constrained heterogeneous environments. Future Generation Computer Systems 108:762–776 Nagurney [1998] Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Nagurney A (1998) Network economics: A variational inequality approach, vol 10. Springer Science & Business Media Nowak [2006] Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Nowak MA (2006) Evolutionary Dynamics: Exploring the Equations of Life. Harvard Univ. Press Raju and Krishnaprasad [2018] Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Raju V, Krishnaprasad P (2018) A Variational Problem on the Probability Simplex. In: 2018 IEEE Conf. on Decision and Control (CDC), IEEE, pp 3522–3528 Samuelson [2016] Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Samuelson L (2016) Game theory in economics and beyond. Journal of Economic Perspectives 30(4):107–130 Sandholm [2001] Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Sandholm WH (2001) Potential games with continuous player sets. Journal of Economic Theory 97(1):81–108 Sandholm [2010] Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Sandholm WH (2010) Population games and evolutionary dynamics. MIT press Sanz-Serna [2016] Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Sanz-Serna JM (2016) Symplectic runge–kutta schemes for adjoint equations, automatic differentiation, optimal control, and more. SIAM Review 58(1):3–33. https://doi.org/10.1137/151002769 Sato and Crutchfield [2003] Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Sato Y, Crutchfield JP (2003) Coupled replicator equations for the dynamics of learning in multiagent systems. Phys Rev E 67:015206 Sato et al [2005] Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Sato Y, Akiyama E, Crutchfield JP (2005) Stability and diversity in collective adaptation. Physica D: Nonlinear Phenomena 210(1):21–57 Savarino and Schnörr [2020] Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Savarino F, Schnörr C (2020) Continuous-Domain Assignment Flows. Europ J Appl Math pp 1–28 Savarino et al [2023] Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Savarino F, Albers P, Schnörr C (2023) On the geometric mechanics of assignment flows for metric data labeling. Information Geometry Schnörr [2020] Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Schnörr C (2020) Assignment Flows. In: Grohs P, Holler M, Weinmann A (eds) Handbook of Variational Methods for Nonlinear Geometric Data. Springer, p 235—260 Schuster and Sigmund [1983] Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Schuster P, Sigmund K (1983) Replicator dynamics. Journal of theoretical biology 100(3):533–538 Schwarz et al [2023] Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Schwarz J, Cassel J, Boll B, et al (2023) Quantum state assignment flows. Entropy 25(9) Sitenko et al [2021] Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Sitenko D, Boll B, Schnörr C (2021) Assignment Flow For Order-Constrained OCT Segmentation. Int J Computer Vision 129:3088–3118 Smith [1982] Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Smith JM (1982) Evolution and the theory of games. In: Did Darwin get it right? Essays on games, sex and evolution. Springer, p 202–215 Smith and Price [1973] Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Smith JM, Price GR (1973) The logic of animal conflict. Nature 246(5427):15–18 Smith et al [2000] Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Smith KE, Kahanpää L, Kekäläinen P, et al (2000) An Invitation to Algebraic Geometry. Springer Taylor and Jonker [1978] Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Taylor PD, Jonker LB (1978) Evolutionary stable strategies and game dynamics. Mathematical biosciences 40(1-2):145–156 Venkateswaran and Gokhale [2019] Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Venkateswaran VR, Gokhale CS (2019) Evolutionary dynamics of complex multiple games. Proceedings of the Royal Society B: Biological Sciences 286(1905):20190900 Zeilmann et al [2020] Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Zeilmann A, Savarino F, Petra S, et al (2020) Geometric Numerical Integration of the Assignment Flow. Inverse Problems 36(3):034004 (33pp) Zeilmann et al [2023] Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Zeilmann A, Petra S, Schnörr C (2023) Learning Linearized Assignment Flows for Image Labeling. J Math Imag Vision 65:164–184 Zern et al [2020] Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Zern A, Zisler M, Petra S, et al (2020) Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment. Journal of Mathematical Imaging and Vision 62(6–7):982–1006 Zern et al [2022] Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Zern A, Zeilmann A, Schnörr C (2022) Assignment flows for data labeling on graphs: convergence and stability. Information Geometry 5(2):355–404 Zisler et al [2020] Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156 Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
- Zisler M, Zern A, Petra S, et al (2020) Self-Assignment Flows for Unsupervised Data Labeling on Graphs. SIAM Journal on Imaging Sciences 13(3):1113–1156
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