Evolutionary Games with Group Selection

Martin Kaae Jensen and Alexandros Rigos

Discussion Papers from Department of Economics, University of Birmingham

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.

Keywords: Evolutionary Game Theory; Evolutionarily Stable Strategy; ESS; Group Selection; Non-random Matching (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Pages: 44 pages
Date: 2012-12
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https://repec.cal.bham.ac.uk/pdf/13-05.pdf

Related works:
Working Paper: Evolutionary Games with Group Selection (2014)
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