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Equilibrium payoffs of finite games

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  • 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.

Suggested Citation

  • Lehrer, Ehud & Solan, Eilon & Viossat, Yannick, 2011. "Equilibrium payoffs of finite games," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 48-53, January.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:1:p:48-53
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    1. 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.
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    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    5. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
    6. David Avis & Gabriel Rosenberg & Rahul Savani & Bernhard Stengel, 2010. "Enumeration of Nash equilibria for two-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 9-37, January.
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    Cited by:

    1. Yehuda John Levy, 2016. "Projections and functions of Nash equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 435-459, March.

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