TY - JOUR

T1 - Equilibrium payoffs of finite games

AU - Lehrer, Ehud

AU - Solan, Eilon

AU - Viossat, Yannick

N1 - Funding Information:
Viossat thanks Bernhard von Stengel, participants to the game theory seminar of the Institut Henri Poincaré, Paris, and to the “Communication and networks in games” workshop in Valencia. He particularly thanks Roberto Lucchetti, Sergiu Hart and John Levy for questions which lead to Sections 4 and 5. PICASSO funding, and the support of the GIP ANR (Croyances Project) and of the Risk Foundation (Groupama Chair) are gratefully acknowledged by Viossat. The work of Solan was partially supported by ISF grant 212/09.

PY - 2011/1/20

Y1 - 2011/1/20

N2 - 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.

AB - 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.

KW - Correlated equilibrium

KW - Equilibrium payoffs

UR - http://www.scopus.com/inward/record.url?scp=79952696707&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2010.10.007

DO - 10.1016/j.jmateco.2010.10.007

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AN - SCOPUS:79952696707

SN - 0304-4068

VL - 47

SP - 48

EP - 53

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

IS - 1

ER -