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Pure strategy equilibria in symmetric two-player zero-sum games

  • Peter Duersch

    ()

  • Jörg Oechssler

    ()

  • Burkhard Schipper

    ()

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.

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File URL: http://hdl.handle.net/10.1007/s00182-011-0302-x
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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 41 (2012)
Issue (Month): 3 (August)
Pages: 553-564

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Handle: RePEc:spr:jogath:v:41:y:2012:i:3:p:553-564
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  1. Alexander Matros & John Duffy & Ted Temzelides, 2006. "Competitive Behavior in Market Games: Evidence and Theory," Working Papers 201, University of Pittsburgh, Department of Economics, revised Sep 2008.
  2. Ana B. Ania, 2005. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Vienna Economics Papers 0601, University of Vienna, Department of Economics.
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  4. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
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  6. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  7. Burkhard Hehenkamp & Wolfgang Leininger & Alex Possajennikov, 2003. "Evolutionary Equilibrium in Tullock Contests: Spite and Overdissipation," Discussion Papers in Economics 03_01, University of Dortmund, Department of Economics.
  8. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  9. Tobias Guse & Burkhard Hehenkamp & Alex Possajennikov, 2008. "On the Equivalence of Nash and Evolutionary Equilibrium in Finite Populations," Discussion Papers 2008-06, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
  10. Tanaka, Yasuhito, 2000. "A finite population ESS and a long run equilibrium in an n players coordination game," Mathematical Social Sciences, Elsevier, vol. 39(2), pages 195-206, March.
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