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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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    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. Konrad, Kai A. & Morath, Florian, 2020. "The Volunteer’s Dilemma in Finite Populations," CEPR Discussion Papers 15536, C.E.P.R. Discussion Papers.
    3. 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.
    4. repec:zbw:rwirep:0497 is not listed on IDEAS
    5. Leininger, Wolfgang, 2019. "Is it really overdissipation? A reassessment of evolutionarily stable behavior in contests," Ruhr Economic Papers 809, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    6. Ana B. Ania & Andreas Wagener, 2021. "Laboratory federalism with public funds sharing," Economic Inquiry, Western Economic Association International, vol. 59(3), pages 1047-1065, July.
    7. Kai A. Konrad & Florian Morath, 2021. "The volunteer’s dilemma in finite populations," Journal of Evolutionary Economics, Springer, vol. 31(4), pages 1277-1290, September.
    8. Ana B. Ania & Andreas Wagener, 2021. "Laboratory federalism with public funds sharing," Economic Inquiry, Western Economic Association International, vol. 59(3), pages 1047-1065, July.
    9. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 0500, University of Heidelberg, Department of Economics.
    10. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 0500, University of Heidelberg, Department of Economics.
    11. Robert Philipowski, 2016. "Spiteful behavior can make everybody better off," Evolutionary and Institutional Economics Review, Springer, vol. 13(1), pages 113-116, June.
    12. Gu, Yiquan & Hehenkamp, Burkhard & Leininger, Wolfgang, 2019. "Evolutionary equilibrium in contests with stochastic participation: Entry, effort and overdissipation," Journal of Economic Behavior & Organization, Elsevier, vol. 164(C), pages 469-485.
    13. Andreas Wagener, 2016. "Evolutionary Stability in Fiscal Competition," CESifo Working Paper Series 5791, CESifo.
    14. 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.
    15. 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(4), pages 1251-1264, November.
    16. Ania, Ana B. & Wagener, Andreas, 2009. "The Open Method of Coordination (OMC) as an Evolutionary Learning Process," Hannover Economic Papers (HEP) dp-416, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    17. 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.
    18. Wagener, Andreas, 2016. "Contests, private provision of public goods and evolutionary stability," Economics Letters, Elsevier, vol. 138(C), pages 34-37.
    19. Hamed Markazi Moghadam, 2020. "Price and non-price competition in an oligopoly: an analysis of relative payoff maximizers," Journal of Evolutionary Economics, Springer, vol. 30(2), pages 507-521, April.
    20. Thomas W. L. Norman, 2021. "Evolutionary stability in the generalized second-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 235-250, February.
    21. 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.
    22. Takuya Iimura & Toshimasa Maruta & Takahiro Watanabe, 2019. "Equilibria in games with weak payoff externalities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 245-258, December.

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    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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