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Pure strategy equilibria in symmetric two-player zero-sum games

  • Peter Duersch

    ()

  • Jörg Oechssler

    ()

  • Burkhard Schipper

    ()

We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. Our findings extend to general two-player zero-sum games using the symmetrization of zero-sum games due to von Neumann. We point out that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of finite population evolutionary stable strategies.

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File URL: http://hdl.handle.net/10.1007/s00182-011-0302-x
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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 41 (2012)
Issue (Month): 3 (August)
Pages: 553-564

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Handle: RePEc:spr:jogath:v:41:y:2012:i:3:p:553-564
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  1. 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.
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