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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 Evolutionary Stable Strategy with Group Selection (ESSGS). These concepts generalize Maynard Smith and Price (1973) to settings with arbitrary matching rules, in particular they reduce, respectively, to Nash equilibrium and ESS when matching is random. NEGS are ESSGS are to the canonical group selection model of evolutionary theory what Nash Equilibrium and ESS are 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 BEGS under some matching rule. Our results are illustrated in Hawk-Dove, Prisoners' dilemma, and Stage Hunt games.

Suggested Citation

  • Martin Kaae Jensen & Alexandros Rigos, 2012. "Evolutionary Games with Group Selection," Discussion Papers 13-05, Department of Economics, University of Birmingham.
    • Handle: RePEc:bir:birmec:13-05
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    Cited by:

    1. Alexandros Rigos & Heinrich H. Nax, 2015. "Assortativity evolving from social dilemmas," Discussion Papers in Economics 15/19, Division of Economics, School of Business, University of Leicester.

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    Keywords

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    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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