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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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    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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