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

Dep. of Economics, Univ. of California Davis, Calif.
Publication Date
  • C72
  • C73
  • Ddc:330
  • Symmetric Two-Player Games
  • Zero-Sum Games
  • Rock-Paper-Scissors
  • Single-Peakedness
  • Quasiconcavity
  • Finite Population Evolutionary Stable Strategy
  • Saddle Point
  • Exact Potential Games


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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