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On the equivalence of Nash and evolutionary equilibrium in finite populations

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  • Hehenkamp, Burkhard
  • Possajennikov, Alex
  • Guse, Tobias

Abstract

This paper provides sufficient and partially necessary conditions for the equivalence of symmetric Nash and evolutionary equilibrium in symmetric games played by finite populations. The conditions are based on generalized constant-sum and "smallness" properties, the latter of which is known from models of perfect competition and large games. The conditions are illustrated on examples including oligopoly games.

Suggested Citation

  • Hehenkamp, Burkhard & Possajennikov, Alex & Guse, Tobias, 2010. "On the equivalence of Nash and evolutionary equilibrium in finite populations," Journal of Economic Behavior & Organization, Elsevier, vol. 73(2), pages 254-258, February.
  • Handle: RePEc:eee:jeborg:v:73:y:2010:i:2:p:254-258
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    References listed on IDEAS

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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. Hehenkamp, B. & Leininger, W. & Possajennikov, A., 2004. "Evolutionary equilibrium in Tullock contests: spite and overdissipation," European Journal of Political Economy, Elsevier, vol. 20(4), pages 1045-1057, November.
    3. Vega-Redondo, Fernando (ed.), 1996. "Evolution, Games, and Economic Behaviour," OUP Catalogue, Oxford University Press, number 9780198774723.
    4. 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.
    5. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 497-516, October.
    6. 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.
    7. Alos-Ferrer, Carlos & Ania, Ana B., 2005. "The asset market game," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 67-90, February.
    8. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
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    Citations

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    Cited by:

    1. Thomas Vallée & Murat Yıldızoğlu, 2013. "Can They Beat the Cournot Equilibrium? Learning with Memory and Convergence to Equilibria in a Cournot Oligopoly," Computational Economics, Springer;Society for Computational Economics, vol. 41(4), pages 493-516, April.
    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. 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.
    5. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 553-564, August.
    6. Wagener, Andreas, 2016. "Contests, private provision of public goods and evolutionary stability," Economics Letters, Elsevier, vol. 138(C), pages 34-37.
    7. Konrad, Kai A. & Morath, Florian, 2016. "Bargaining with incomplete information: Evolutionary stability in finite populations," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 118-131.
    8. Moghadam, Hamed M., 2015. "Price and non-price competition in oligopoly: An analysis of relative payoff maximizers," Ruhr Economic Papers 575, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    9. Andreas Wagener, 2016. "Evolutionary Stability in Fiscal Competition," CESifo Working Paper Series 5791, CESifo Group Munich.
    10. repec:zbw:rwirep:0497 is not listed on IDEAS
    11. Leininger, Wolfgang & Moghadam, Hamed M., 2014. "Evolutionary Stability in Asymmetric Oligopoly. A Non-Walrasian Result," Ruhr Economic Papers 497, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    12. Takuya Iimura & Takahiro Watanabe, 2016. "Pure strategy equilibrium in finite weakly unilaterally competitive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 719-729, August.
    13. Wolfgang Leininger & Hamed Moghadam, 2014. "Evolutionary Stability in Asymmetric Oligopoly. A Non-Walrasian Result," Ruhr Economic Papers 0497, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.

    More about this item

    Keywords

    Nash equilibrium Evolutionary stability Finite populations;

    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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