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Pure Saddle Points and Symmetric Relative Payoff Games

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

No 500, Working Papers from University of Heidelberg, 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 (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Date: 2010-03-30
New Economics Papers: this item is included in nep-evo and nep-gth
Note: This paper is part of http://archiv.ub.uni-heidelberg.de/volltextserver/view/schriftenreihen/sr-3.html
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Citations: View citations in EconPapers (2)

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