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International Journal of Game Theory

, Volume 41, Issue 3, pp 553–564 | Cite as

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

  • Peter Duersch
  • Jörg Oechssler
  • Burkhard C. SchipperEmail author
Article

Abstract

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.

Keywords

Symmetric two-player games Zero-sum games Rock-paper-scissors Single-peakedness Quasiconcavity Finite population evolutionary stable strategy Saddle point Exact potential games 

JEL Classification

C72 C73 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Peter Duersch
    • 1
  • Jörg Oechssler
    • 1
  • Burkhard C. Schipper
    • 2
    Email author
  1. 1.Department of EconomicsUniversity of HeidelbergHeidelbergGermany
  2. 2.Department of EconomicsUniversity of California, DavisDavisUSA

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