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- Title
Pure strategy equilibria in symmetric two-player zero-sum games.
- Authors
Duersch, Peter; Oechssler, Jörg; Schipper, Burkhard
- Abstract
We observe that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. Our findings extend to general two-player zero-sum games using the symmetrization of zero-sum games due to von Neumann. We point out 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 finite population evolutionary stable strategies.
- Subjects
ECONOMIC equilibrium; ZERO sum games; GENERALIZATION; EXISTENCE theorems; METHOD of steepest descent (Numerical analysis); ROCK-paper-scissors (Game); MATHEMATICAL analysis
- Publication
International Journal of Game Theory, 2012, Vol 41, Issue 3, p553
- ISSN
0020-7276
- Publication type
Article
- DOI
10.1007/s00182-011-0302-x