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

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Abstract
It is well known that the rockpaperscissors game has no pure saddle point. We show that this holds more generally: A symmetric twoplayer zerosum game has a pure saddle point if and only if it is not a generalized rockpaperscissors game. Moreover, we show that every finite symmetric quasiconcave twoplayer zerosum 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 twoplayer zerosum games coincides with the class of relative payoff games associated with symmetric twoplayer 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 
Language:  English 
Keywords:  symmetric twoplayer games; zerosum games; RockPaperScissors; singlepeakedness; 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 
Item ID:  20864 
Depositing User:  Burkhard C Schipper 
Date Deposited:  22 Feb 2010 11:28 
Last Modified:  21 Feb 2016 07:49 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/20864 