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Pure Saddle Points and Symmetric Relative Payoff Games

  • Peter Duersch
  • Joerg Oechssler
  • Burkhard C. Schipper

    (Department of Economics, University of California Davis)

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 California, Davis, Department of Economics in its series Working Papers with number 104.

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Length: 20
Date of creation: 21 Feb 2010
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Handle: RePEc:cda:wpaper:10-4
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