Pure strategy equilibria in symmetric two-player zero-sum games |
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Authors: | Peter?Duersch J?rg?Oechssler Email author" target="_blank">Burkhard?C?SchipperEmail author |
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Institution: | 1.Department of Economics,University of Heidelberg,Heidelberg,Germany;2.Department of Economics,University of California, Davis,Davis,USA |
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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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