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Symmetric games with only asymmetric equilibria

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  • Fey, Mark

Abstract

It is known that not every symmetric game has a symmetric equilibrium because there are examples of symmetric games that fail to have any equilibria at all. But this leads to the following question: If a symmetric game has a Nash equilibrium, does it have a symmetric Nash equilibrium? In this Note, we show that the answer to this question is no by providing two examples of symmetric games that have only asymmetric equilibria.

Suggested Citation

  • Fey, Mark, 2012. "Symmetric games with only asymmetric equilibria," Games and Economic Behavior, Elsevier, vol. 75(1), pages 424-427.
  • Handle: RePEc:eee:gamebe:v:75:y:2012:i:1:p:424-427
    DOI: 10.1016/j.geb.2011.09.008
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    References listed on IDEAS

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    Cited by:

    1. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0540-z is not listed on IDEAS
    2. Dimitrios Xefteris & Didier Laussel & Michel Le Breton, 2017. "Simple centrifugal incentives in spatial competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 357-381, May.
    3. Xefteris, Dimitrios, 2014. "Mixed equilibria in runoff elections," Games and Economic Behavior, Elsevier, vol. 87(C), pages 619-623.
    4. Shiran Rachmilevitch, 2016. "Symmetry and approximate equilibria in games with countably many players," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 709-717, August.
    5. Antoni Bosch-Domènech & Joaquin Silvestre, 2017. "Experiment-inspired comments on John Roemer's theory of cooperation," Economics Working Papers 1593, Department of Economics and Business, Universitat Pompeu Fabra.
    6. Xefteris, Dimitrios, 2015. "Symmetric zero-sum games with only asymmetric equilibria," Games and Economic Behavior, Elsevier, vol. 89(C), pages 122-125.
    7. Rachmilevitch, Shiran, 2016. "Approximate equilibria in strongly symmetric games," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 52-57.

    More about this item

    Keywords

    Symmetric game; Symmetric equilibrium; Zero-sum game;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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