Evolutionary Games with Group Selection

Martin Jensen and Alexandros Rigos

No 14/09, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester

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.

Keywords: Evolutionary Game Theory; Evolutionarily Stable Strategy; ESS; Group Selection; Non-random Matching; Trait-group Model; Haystack Model. (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Date: 2014-07
New Economics Papers: this item is included in nep-cdm, nep-evo, nep-gth, nep-hpe and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Working Paper: Evolutionary Games with Group Selection (2012)
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