Equilibrium payoffs of finite games

Lehrer, Ehud; Solan, Eilon; Viossat, Yannick

Lehrer, Ehud; Solan, Eilon; Viossat, Yannick (2011), Equilibrium payoffs of finite games, Journal of Mathematical Economics, 47, 1, p. 48-53. http://dx.doi.org/10.1016/j.jmateco.2010.10.007

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00361914/en/

Date

2011

Journal name

Journal of Mathematical Economics

Volume

Number

Publisher

Elsevier

Pages

48-53

Abstract (EN)

We study the structure of the set of equilibrium payoffs in finite games, both for Nash equilibrium and correlated equilibrium. A nonempty subset of R^2 is shown to be the set of Nash equilibrium payoffs of a bimatrix game if and only if it is a finite union of rectangles. Furthermore, we show that for any nonempty finite union of rectangles U and any polytope P in R^2 containing U, there exists a bimatrix game with U as set of Nash equilibrium payoffs and P as set of correlated equilibrium payoffs. The n-player case and the robustness of this result to perturbation of the payoff matrices are also studied.

Subjects / Keywords

equilibrium payoffs; correlated equilibrium; Optimization and Control

JEL

C72 - Noncooperative Games