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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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    Cited by:

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    7. Davidson Cheng, 2022. "Asymmetric Equilibria in Symmetric Multiplayer Prisoners Dilemma Supergames," Papers 2205.13772, arXiv.org.
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    More about this item

    Keywords

    Symmetric game; Symmetric equilibrium; Zero-sum game;
    All these keywords.

    JEL classification:

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

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