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Article Dans Une Revue Journal of Mathematical Economics Année : 2011

Equilibrium payoffs in finite games

Ehud Lehrer
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Eilon Solan
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Résumé

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.
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Dates et versions

hal-00361914 , version 1 (16-02-2009)

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Ehud Lehrer, Eilon Solan, Yannick Viossat. Equilibrium payoffs in finite games. Journal of Mathematical Economics, 2011, 47, pp.48-53. ⟨10.1016/j.jmateco.2010.10.007⟩. ⟨hal-00361914⟩
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