Equilibrium payoffs in finite games
Optimization and Control
2009-02-17 v1
Abstract
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.
Cite
@article{arxiv.0902.2770,
title = {Equilibrium payoffs in finite games},
author = {Ehud Lehrer and Eilon Solan and Yannick Viossat},
journal= {arXiv preprint arXiv:0902.2770},
year = {2009}
}