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Evolutionary Games with Group Selection

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  • Martin Kaae Jensen
  • Alexandros Rigos

Abstract

This paper introduces two new concepts in evolutionary game theory: Nash equilibrium with Group Selection (NEGS) and Evolutionarily Stable Strategy with Group Selection (ESSGS). These concepts generalize Maynard Smith and Price (1973) to settings with arbitrary matching rules, inparticular they reduce, respectively, to Nash equilibrium and ESS when matching is random. NEGS and ESSGS are to the canonical group selection model of evolutionary theory what Nash Equilibrium and ESS are to the standard replicator dynamics: any NEGS is a steady state, any stable steady state is a NEGS, and any ESSGS is asymptotically stable. We exploit this to prove what may be called “the second welfare theorem of evolution”: Any evolutionary optimum will be a NEGS under some matching rule. Our results are illustrated in Hawk-Dove, Prisoners’ dilemma, and Stag Hunt games.

Suggested Citation

  • Martin Kaae Jensen & Alexandros Rigos, 2014. "Evolutionary Games with Group Selection," Discussion Papers in Economics 14/09, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:14/09
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    References listed on IDEAS

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    Cited by:

    1. Nax, Heinrich H. & Rigos, Alexandros, 2015. "Assortativity evolving from social dilemmas," LSE Research Online Documents on Economics 65447, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    Evolutionary Game Theory; Evolutionarily Stable Strategy; ESS; Group Selection; Non-random Matching; Trait-group Model; Haystack Model.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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