Computing Nash Equilibria and Evolutionarily Stable States of Evolutionary Games

Jiawei Li, Graham Kendall, Robert John

Research output: Journal PublicationArticlepeer-review

41 Citations (Scopus)


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.

Original languageEnglish
Article number7296643
Pages (from-to)460-469
Number of pages10
JournalIEEE Transactions on Evolutionary Computation
Issue number3
Publication statusPublished - Jun 2016


  • Evolutionary game theory
  • Nash equilibrium
  • evolutionary stability
  • folk theorem
  • iterated prisoner's dilemma

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics


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