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Pure Strategy Equilibria in Symmetric Two-Player Zero-Sum Games

  • Peter Duersch
  • Joerg Oechssler
  • Burkhard Schipper

    (Department of Economics, University of California Davis)

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://wp.econ.ucdavis.edu/10-21.pdf
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Paper provided by University of California, Davis, Department of Economics in its series Working Papers with number 1021.

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Length: 15
Date of creation: 23 Nov 2010
Date of revision:
Handle: RePEc:cda:wpaper:10-21
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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.
  3. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Hehenkamp, B. & Leininger, W. & Possajennikov, A., 2004. "Evolutionary equilibrium in Tullock contests: spite and overdissipation," European Journal of Political Economy, Elsevier, vol. 20(4), pages 1045-1057, November.
  5. Radzik, Tadeusz, 1991. "Saddle Point Theorems," International Journal of Game Theory, Springer, vol. 20(1), pages 23-32.
  6. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  7. Branzei, Rodica & Mallozzi, Lina & Tijs, Stef, 2003. "Supermodular games and potential games," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 39-49, February.
  8. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2012. "Unbeatable Imitation," Working Papers 125, University of California, Davis, Department of Economics.
  9. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  10. Alex Possajennikov, 2001. "Evolutionary Foundations of Aggregate-Taking Behavior," Discussion Papers in Economics 01_10, University of Dortmund, Department of Economics.
  11. 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.
  12. Brânzei, R. & Mallozzi, L. & Tijs, S.H., 2003. "Supermodular games and potential games," Other publications TiSEM 87c16860-0596-4448-808d-c, Tilburg University, School of Economics and Management.
  13. 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.
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