Equilibrium payoffs of finite games

Ehud Lehrer, Eilon Solan, Yannick Viossat

Research output: Contribution to journalArticlepeer-review


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 R2, 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.

Original languageEnglish
Pages (from-to)48-53
Number of pages6
JournalJournal of Mathematical Economics
Issue number1
StatePublished - 20 Jan 2011


  • Correlated equilibrium
  • Equilibrium payoffs

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics
  • Applied Mathematics


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