Template-Type: ReDIF-Paper 1.0
Author-Name: Burkhard C. Schipper
Author-Name-First: Burkhard C.
Author-Name-Last: Schipper
Author-Name: Peter Duersch
Author-Name-First: Peter
Author-Name-Last: Duersch
Author-Name: Joerg Oechssler
Author-Name-First: Joerg
Author-Name-Last: Oechssler
Author-Workplace-Name: Department of Economics, University of California Davis
Title: Pure Saddle Points and Symmetric Relative Payoff Games
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 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.
Length: 20
File-URL: https://repec.dss.ucdavis.edu/files/74e8Ar3RjaDus7W5Tbe8tMWx/10-4.pdf
File-Format: application/pdf
Number: 301
Classification-JEL: C72, C73
KeyWords: 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
Creation-Date: 20100220
Handle: RePEc:cda:wpaper:301