%0 Generic
%A Duersch, Peter
%A Oechssler, Jörg
%A Schipper, Burkhard C.
%D 2010
%F heidok:10545
%K Symmetric two-player games , zero-sum games , Rock-Paper-Scissors , single-peakedness , quasiconcavity
%R 10.11588/heidok.00010545
%T Pure Saddle Points and Symmetric Relative Payoff Games
%U https://archiv.ub.uni-heidelberg.de/volltextserver/10545/
%X 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.