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Computing Nash equilibria and evolutionarily stable states of evolutionary games

Li, Jiawei; Kendall, Graham; John, Robert

Authors

Jiawei Li

Robert John robert.john@nottingham.ac.uk



Abstract

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.

Journal Article Type Article
Journal IEEE Transactions on Evolutionary Computation
Print ISSN 1089-778X
Electronic ISSN 1089-778X
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 20
Issue 3
APA6 Citation Li, J., Kendall, G., & John, R. (in press). Computing Nash equilibria and evolutionarily stable states of evolutionary games. IEEE Transactions on Evolutionary Computation, 20(3), doi:10.1109/TEVC.2015.2490076
DOI https://doi.org/10.1109/TEVC.2015.2490076
Keywords Evolutionary game theory, evolutionary stability, folk theorem, iterated prisoner’s dilemma, Nash equilibrium
Publisher URL http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7296643
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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