Duersch, Peter Oechssler, Joerg Schipper, Burkhard C.
Year of Publication:
Working Paper No. 10-21
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.
symmetric two-player games zero-sum games Rock-Paper-Scissors single-peakedness quasiconcavity finite population evolutionary stable strategy saddle point exact potential games