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Pure Saddle Points and Symmetric Relative Payoff Games

Duersch, Peter and Oechssler, Jörg and Schipper, Burkhard C.

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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.

Item Type: Working paper
Date Deposited: 30. Mar 2010 16:09
Date: 2010
Faculties / Institutes: The Faculty of Economics and Social Studies > Alfred-Weber-Institut for Economics
Subjects: 330 Economics
Uncontrolled Keywords: Symmetric two-player games , zero-sum games , Rock-Paper-Scissors , single-peakedness , quasiconcavity
Schriftenreihe ID: Discussion Paper Series / University of Heidelberg, Department of Economics
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