Pure strategy equilibria in symmetric two-player zero-sum games - Peter Duersch; Joerg Oechssler; Burkhard C. Schipper (University of California, Department of Economics, 2010)
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.
Keywords: C72; C73; 330; symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity; finite population evolutionary stable strategy; saddle point; exact potential games