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| Title: | | Pure saddle points and symmetric relative payoff games  |
| Authors: | | Duersch, Peter Oechssler, Jörg Schipper, Burkhard C. |
| Issue Date: | | 2010 |
| Series/Report no.: | | Working Papers, University of California, Department of Economics 10,4 |
| Abstract: | | 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. |
| Subjects: | | 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 |
| JEL: | | C72 C73 |
| Document Type: | | Working Paper |
| Appears in Collections: | | Working Papers, Department of Economics, UC Davis
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