TY  - GEN
ID  - heidok10545
KW  - Symmetric two-player games 
KW  -  zero-sum games 
KW  -  Rock-Paper-Scissors 
KW  -  single-peakedness 
KW  -  quasiconcavity
TI  - Pure Saddle Points and Symmetric Relative Payoff Games
Y1  - 2010///
AV  - public
N2  - 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.
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/10545/
A1  - Duersch, Peter
A1  - Oechssler, Jörg
A1  - Schipper, Burkhard C.
ER  -