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Equilibrium payoffs of finite games

  • Lehrer, Ehud
  • Solan, Eilon
  • Viossat, Yannick

Abstract We study the structure of the set of equilibrium payoffs in finite games, both for Nash and correlated equilibria. In the two-player case, we obtain a full characterization: if U and P are subsets of , then there exists a bimatrix game whose sets of Nash and correlated equilibrium payoffs are, respectively, U and P, if and only if U is a finite union of rectangles, P is a polytope, and P contains U. The n-player case and the robustness of the result to perturbation of the payoff matrices are also studied. We show that arbitrarily close games may have arbitrarily different sets of equilibrium payoffs. All existence proofs are constructive.

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Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 47 (2011)
Issue (Month): 1 (January)
Pages: 48-53

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Handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:48-53
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
  3. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
  4. Yannick Viossat, 2008. "Is Having a Unique Equilibrium Robust?," Post-Print hal-00361891, HAL.
  5. David Avis & Gabriel Rosenberg & Rahul Savani & Bernhard Stengel, 2010. "Enumeration of Nash equilibria for two-player games," Economic Theory, Springer, vol. 42(1), pages 9-37, January.
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