Computing Nash Equilibria and Evolutionarily Stable States of Evolutionary Games

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. https://doi.org/10.1109/TEVC.2015.2490076

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.

Keywords
Evolutionary game theory; Nash equilibrium; Nash equilibrium (NE); evolutionary stability; folk theorem; iterated prisoner’s dilemma

Journal
IEEE Transactions on Evolutionary Computation: Volume 20, Issue 3