Pure Saddle Points and Symmetric Relative Payoff Games

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

No 301, Working Papers from University of California, Davis, Department of Economics

Abstract: It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting 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 a finite population evolutionary stable strategies.

Keywords: symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity; finite population evolutionary stable strategy; increasing differences; decreasing differences; potentials; additive separability (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Pages: 20
Date: 2010-02-20
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Pure Saddle Points and Symmetric Relative Payoff Games (2010)
Working Paper: Pure Saddle Points and Symmetric Relative Payoff Games (2010)
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