Pure strategy equilibria in symmetric two-player zero-sum games
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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.
KeywordsSymmetric two-player games Zero-sum games Rock-paper-scissors Single-peakedness Quasiconcavity Finite population evolutionary stable strategy Saddle point Exact potential games
JEL ClassificationC72 C73
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