Duersch, Peter Oechssler, Jörg Schipper, Burkhard C.
Year of Publication:
Working Paper 10-4
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 suffiient 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.
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