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

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.

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Correspondence to Burkhard C. Schipper.

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Duersch, P., Oechssler, J. & Schipper, B.C. Pure strategy equilibria in symmetric two-player zero-sum games. Int J Game Theory 41, 553–564 (2012). https://doi.org/10.1007/s00182-011-0302-x

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  • DOI: https://doi.org/10.1007/s00182-011-0302-x

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