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Nash Equilibrium and Evolutionary Stability in Large and Finite Populations

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  • Vincent P. Crawford

Abstract

This paper studies the correspondence between Nash equilibrium and evolutionary stability in large and finite populations. Whenever the payoff function of the game that describes the simultaneous interaction of the individuals in the population, and thereby determines their fitnesses, is sufficiently continuous, an evolutionarily stable strategy (ESS) in a large population corresponds to a symmetric Nash equilibrium in that game, and a strict, symmetric Nash equilibrium in that game corresponds to a large-population ESS. This correspondence continues to hold, approximately, in finite populations; and it holds exactly for strict pure-strategy equilibria in sufficiently large finite populations.

Suggested Citation

  • Vincent P. Crawford, 1992. "Nash Equilibrium and Evolutionary Stability in Large and Finite Populations," Annals of Economics and Statistics, GENES, issue 25-26, pages 299-313.
    • Handle: RePEc:adr:anecst:y:1992:i:25-26:p:299-313
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    File URL: http://www.jstor.org/stable/20075868
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    Cited by:

    1. Chatterjee, Arko & Rao, K.S. Mallikarjuna & Sarangi, Sudipta, 2023. "Evolutionary stability for games played on networks," Economics Letters, Elsevier, vol. 229(C).

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