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Title:Pure saddle points and symmetric relative payoff games PDF Logo
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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