Pure Saddle Points and Symmetric Relative Payoff Games

Duersch, Peter and Oechssler, Joerg and Schipper, Burkhard C (2010): Pure Saddle Points and Symmetric Relative Payoff Games.

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: MPRA Paper
• Language: English
• Keywords: symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity; finite population evolutionary stable strategy; increasing differences; decreasing differences; potentials; additive separability
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

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