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arXiv · 1003.4277

Pure Saddle Points and Symmetric Relative Payoff Games

Peter Duersch·Joerg Oechssler·Burkhard C. Schipper
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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.

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Peter Duersch, Joerg Oechssler, Burkhard C. Schipper. 2010-03-22. Pure Saddle Points and Symmetric Relative Payoff Games. https://doi.org/10.1007/s00182-011-0302-x

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