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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Computing Nash Equilibria and Evolutionarily Stable States of Evolutionary Games
Author(s): Li, Jiawei
Kendall, Graham
John, Robert
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Keywords: Evolutionary game theory
Nash equilibrium
Nash equilibrium (NE)
evolutionary stability
folk theorem
iterated prisoner’s dilemma
Issue Date: Jun-2016
Date Deposited: 14-Jun-2016
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), pp. 460-469.
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.
DOI Link: 10.1109/TEVC.2015.2490076
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