Computing Nash Equilibria and Evolutionarily Stable States of Evolutionary Games

Li, Jiawei; Kendall, Graham; John, Robert

Abstract

© 2015 IEEE. Stability analysis is an important research direction in evolutionary game theory. Evolutionarily stable states have a close relationship with Nash equilibria of repeated games, which are characterized by the folk theorem. When applying the folk theorem, one needs to compute the minimax profile of the game in order to find Nash equilibria. Computing the minimax profile is an NP-hard problem. In this paper, we investigate a new methodology to compute evolutionary stable states based on the level-k equilibrium, a new refinement of Nash equilibrium in repeated games. A level-k equilibrium is implemented by a group of players who adopt reactive strategies and who have no incentive to deviate from their strategies simultaneously. Computing the level-k equilibria is tractable because the minimax payoffs and strategies are not needed. As an application, this paper develops a tractable algorithm to compute the evolutionarily stable states and the Pareto front of n-player symmetric games. Three games, including the iterated prisoner's dilemma, are analyzed by means of the proposed methodology.

Citation

Li, J., Kendall, G., & John, R. (2016). Computing Nash Equilibria and Evolutionarily Stable States of Evolutionary Games. IEEE Transactions on Evolutionary Computation, 20(3), 460-469. https://doi.org/10.1109/TEVC.2015.2490076

• Journal Article Type: Article
• Acceptance Date: Oct 5, 2015
• Online Publication Date: Oct 12, 2015
• Publication Date: 2016-06
• Deposit Date: Oct 12, 2015
• Publicly Available Date: Oct 12, 2015
• Journal: IEEE Transactions on Evolutionary Computation
• Print ISSN: 1089-778X
• Electronic ISSN: 1941-0026
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 20
• Issue: 3
• Pages: 460-469
• DOI: https://doi.org/10.1109/TEVC.2015.2490076
• Keywords: Evolutionary game theory, evolutionary stability, folk theorem, iterated prisoner’s dilemma, Nash equilibrium
• Public URL: https://nottingham-repository.worktribe.com/output/764047
• Publisher URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7296643