Duersch, Peter and Oechssler, Joerg and Schipper, Burkhard C (2010): Pure Saddle Points and Symmetric Relative Payoff Games.
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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|
|Original Title:||Pure Saddle Points and Symmetric Relative Payoff Games|
|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
|Depositing User:||Burkhard C Schipper|
|Date Deposited:||22. Feb 2010 11:28|
|Last Modified:||01. Mar 2013 10:44|
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