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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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    References listed on IDEAS

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    1. Simon Gachter & Ernst Fehr, 2000. "Cooperation and Punishment in Public Goods Experiments," American Economic Review, American Economic Association, vol. 90(4), pages 980-994, September.
    2. Wolfgang Leininger, 2006. "Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 713-719, November.
    3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    4. Larry Samuelson, 2002. "Evolution and Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 47-66, Spring.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. Ingela Alger & Jörgen W. Weibull, 2010. "Kinship, Incentives, and Evolution," American Economic Review, American Economic Association, vol. 100(4), pages 1725-1758, September.
    7. Ben Cooper & Chris Wallace, 2004. "Group selection and the evolution of altruism," Oxford Economic Papers, Oxford University Press, vol. 56(2), pages 307-330, April.
    8. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    9. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
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    11. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
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    Cited by:

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

    More about this item

    Keywords

    Evolutionary Game Theory; Evolutionarily Stable Strategy; ESS; Group Selection; Non-random Matching;

    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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