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Evolutionary Games with Group Selection

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number 13-05.

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Length: 44 pages
Date of creation: Dec 2012
Date of revision:
Handle: RePEc:bir:birmec:13-05

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Postal: Edgbaston, Birmingham, B15 2TT
Web page: http://www.economics.bham.ac.uk
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Related research

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

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References

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  1. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
  2. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  4. Larry Samuelson, 2002. "Evolution and Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 47-66, Spring.
  5. Eshel, Ilan & Samuelson, Larry & Shaked, Avner, 1998. "Altruists, Egoists, and Hooligans in a Local Interaction Model," American Economic Review, American Economic Association, vol. 88(1), pages 157-79, March.
  6. Ernst Fehr & Simon Gaechter, 1999. "Cooperation and Punishment in Public Goods Experiments," CESifo Working Paper Series 183, CESifo Group Munich.
  7. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
  8. Wolfgang Leininger, 2006. "Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games," Economic Theory, Springer, vol. 29(3), pages 713-719, November.
  9. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
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