Pure Strategy Equilibria in Symmetric Two-Player Zero-Sum Games

Burkhard Schipper, Peter Duersch and Jörg Oechssler
Authors registered in the RePEc Author Service: Peter Dürsch

No 240, Working Papers from University of California, Davis, Department of Economics

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.

Keywords: Symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity; finite population evolutionary stable strategy; saddle point; exact potential games (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Pages: 15
Date: 2010-11-22
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Pure strategy equilibria in symmetric two-player zero-sum games (2012)
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