2000 character limit reached
Nash implementation in a many-to-one matching market
Published 23 May 2023 in econ.TH | (2305.13956v3)
Abstract: In a many-to-one matching market, we analyze the matching game induced by a stable rule when firms' choice function satisfy substitutability. We show that any stable rule implements the individually rational correspondence in Nash equilibrium when both sides of the market play strategically. Moreover, when only workers play strategically and firms' choice functions satisfy the law of aggregate demand, we show that the firm-optimal stable rule implements the stable correspondence in Nash equilibrium.
- Alcalde, J. (1996): “Implementation of stable solutions to marriage problems,” Journal of Economic Theory, 69, 240–254.
- Alcalde, J. and A. Romero Medina (2000): “Simple Mechanisms to Implement the Core of College Admissions Problems,” Games and Economic Behavior, 31, 294–302.
- Alkan, A. (2002): “A class of multipartner matching markets with a strong lattice structure,” Economic Theory, 19, 737–746.
- Blair, C. (1988): “The lattice structure of the set of stable matchings with multiple partners,” Mathematics of Operations Research, 13, 619–628.
- Crawford, V. P. (1991): “Comparative statics in matching markets,” Journal of Economic Theory, 54, 389–400.
- Dubins L. E. and D. A. Freedman (1981): “Machiavelli and the Gale-Shapley algorithm,” The American Mathematical Monthly, 88, 485–494.
- Ehlers L. (2004): “Monotonic and implementable solutions in generalized matching problems,” Journal of Economic Theory, 114, 358–369.
- Gale, D. and L. Shapley (1962): “College admissions and the stability of marriage,” The American Mathematical Monthly, 69, 9–15.
- Haake, C. J. and B. Klaus (2009): “Monotonicity and Nash implementation in matching markets with contracts,” Economic Theory, 41, 393–410.
- Hatfield, J. and P. Milgrom (2005): “Matching with contracts,” American Economic Review, 95, 913–935.
- Kara, T. and T. Sönmez (1996): “Nash implementation of matching rules,” Journal of Economic Theory, 68, 425–439.
- Kara, T. and T. Sönmez (1997): “Implementation of college admission rules,” Economic Theory, 9, 197–218.
- Kelso, A., and V. Crawford (1982): “Job matching, coalition formation, and gross substitutes,” Econometrica: Journal of the Econometric Society, 50, 1483–1504.
- Kojima, F. (2012): “The "rural hospital theorem" revisited,” International Journal of Economic Theory, 8, 67–76.
- Manasero, P., and J. Oviedo (2022): “General manipulability theorem for a matching model” arXiv preprint arXiv:2210.06549.
- Martínez, R., J. Massó, A. Neme, and J. Oviedo (2000): “Single agents and the set of many-to-one stable matchings,” Journal of Economic Theory, 91, 91–105.
- Martínez, R., J. Massó, A. Neme, and J. Oviedo (2004): “On group strategy-proof mechanisms for a many-to-one matching model,” International Journal of Game Theory, 33, 115–128.
- Maskin, E. (1977): “Nash equilibrium and welfare optimality,” mimeo, MIT.
- Maskin, E. (1999): “Nash equilibrium and welfare optimality,” Review of Economic Studies, 66, 23–38.
- McVitie, D. and L. Wilson (1971): “The stable marriage problem,” Communications of the ACM, 14, 486–490.
- Moore, J. and R. Repullo (1990): “Nash implementation: a full characterization,” Econometrica, 58, 1083–1099.
- Roth, A. (1982): “The economics of matching: stability and incentives,” Mathematics of Operations Research, 7, 617–628.
- Roth, A. (1984): “The evolution of the labor market for medical interns and residents: a case study in game theory,” Journal of Political Economy, 92, 991–1016.
- Roth, A. (1985): “The college admissions problem is not equivalent to the marriage problem,” Journal of Economic Theory, 36, 277–288.
- Sotomayor, M. (1996): “Admission mechanisms of students to colleges,” A game-theoretic modeling and analysis. Braz Rev Econ, 16, 25–63.
- Sotomayor, M. (1999): “Three remarks on the many-to-many stable matching problem,” Mathematical Social Sciences, 38, 55–70.
- Sotomayor, M. (2008): “The stability of the equilibrium outcomes in the admission games induced by stable matching rules,” International Journal of Game Theory, 36, 621–640.
- Sotomayor, M. (2012): “A further note on the college admission game,” International Journal of Game Theory, 41, 179–193.
- Yamato, T. (1992): “On Nash implementation of social choice correspondences,” Games and Economic Behavior, 4, 484–492.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.