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Pure Saddle Points and Symmetric Relative Payoff Games

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

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.

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Paper provided by University of Heidelberg, Department of Economics in its series Working Papers with number 0500.

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Date of creation: 30 Mar 2010
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Handle: RePEc:awi:wpaper:0500

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Keywords: Symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity;

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References

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  1. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
  2. Wolfgang Leininger, 2006. "Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games," Economic Theory, Springer, vol. 29(3), pages 713-719, November.
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Cited by:
  1. Peter Duersch & Joerg Oechssler & Burkhard C. Schipper, 2011. "Unbeatable Imitation," Working Papers 103, University of California, Davis, Department of Economics.

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