Steering control of payoff-maximizing players in adaptive learning dynamics

Abstract: Evolutionary game theory provides a mathematical foundation for cross-disciplinary fertilization, especially for integrating ideas from artificial intelligence and game theory. Such integration offers a transparent and rigorous approach to complex decision-making problems in a variety of important contexts, ranging from evolutionary computation to machine behavior. Despite the astronomically huge individual behavioral strategy space for interactions in the iterated Prisoner's Dilemma (IPD) games, the so-called Zero-Determinant (ZD) strategies is a set of rather simple memory-one strategies yet can unilaterally set a linear payoff relationship between themselves and their opponent. Although the witting of ZD strategies gives players an upper hand in the IPD games, we find and characterize unbending strategies that can force ZD players to be fair in their own interest. Moreover, our analysis reveals the ubiquity of unbending properties in common IPD strategies which are previously overlooked. In this work, we demonstrate the important steering role of unbending strategies in fostering fairness and cooperation in pairwise interactions. Our results will help bring a new perspective by means of combining game theory and multi-agent learning systems for optimizing winning strategies that are robust to noises, errors, and deceptions in non-zero-sum games.