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On the Equivalence of Nash and Evolutionary Equilibrium in Finite Populations

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  • Tobias Guse

    (Department of Economics and Social Sciences, University of Dortmund)

  • Burkhard Hehenkamp

    ()
    (Department of Economics and Social Sciences, University of Dortmund)

  • Alex Possajennikov

    ()
    (School of Economics, University of Nottingham)

Abstract

This paper provides sufficient and partially necessary conditions for the equivalence of Nash and evolutionary equilibrium in symmetric games played by finite populations. The focus is on symmetric equilibria in pure strategies. The conditions are based on properties of the payoff function that generalize the constant-sum property and the ”smallness” property, the latter of which is known from models of perfect competition and non-atomic, anonymous, or large games. The conditions are illustrated on examples of Bertrand and Cournot oligopoly games.

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Bibliographic Info

Paper provided by The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham in its series Discussion Papers with number 2008-06.

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Date of creation: Apr 2008
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Handle: RePEc:cdx:dpaper:2008-06

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Keywords: Nash equilibrium; Evolutionary stability; Finite populations;

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References

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  1. Tanaka, Yasuhito, 2000. "Stochastically stable states in an oligopoly with differentiated goods: equivalence of price and quantity strategies," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 235-253, October.
  2. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  3. Burkhard Hehenkamp & Wolfgang Leininger & Alex Possajennikov, 2003. "Evolutionary Equilibrium in Tullock Contests: Spite and Overdissipation," Discussion Papers in Economics 03_01, University of Dortmund, Department of Economics.
  4. Ania, Ana B., 2008. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 472-488, March.
  5. Carlos Alós-Ferrer & Ana B. Ania, 2003. "The Asset Market Game," Vienna Economics Papers 0320, University of Vienna, Department of Economics.
  6. Schaffer, Mark E., 1989. "Are profit-maximisers the best survivors? : A Darwinian model of economic natural selection," Journal of Economic Behavior & Organization, Elsevier, vol. 12(1), pages 29-45, August.
  7. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
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Cited by:
  1. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer, vol. 41(3), pages 553-564, August.
  2. Ania, Ana B. & Wagener, Andreas, 2009. "The Open Method of Coordination (OMC) as an Evolutionary Learning Process," Discussion Papers in Economics 10332, University of Munich, Department of Economics.
  3. Duersch, Peter & Oechssler, Joerg & Schipper, Burkhard C, 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," MPRA Paper 20864, University Library of Munich, Germany.
  4. Thomas Vallée & Murat Yıldızoğlu, 2013. "Can They Beat the Cournot Equilibrium? Learning with Memory and Convergence to Equilibria in a Cournot Oligopoly," Computational Economics, Society for Computational Economics, vol. 41(4), pages 493-516, April.
  5. Andreas Wagener, 2013. "Tax Competition, Relative Performance, And Policy Imitation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 1251-1264, November.

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