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 -