Structure of extreme correlated equilibria: a zero-sum example and its implications
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Author(s)
Parrilo, Pablo A.
Stein, Noah Daniel
Ozdaglar, Asuman E.
Date Issued
January 2011
Journal
International Journal of Game Theory
Publisher
Springer-Verlag
Citation
Stein, Noah D., Asuman Ozdaglar, and Pablo A. Parrilo. “Structure of Extreme Correlated Equilibria: a Zero-Sum Example and Its Implications.” Int J Game Theory 40, no. 4 (January 4, 2011): 749–767.
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Author's final manuscript
Abstract
We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure of its extreme points can be quite complicated. In finite games the ratio of extreme correlated to extreme Nash equilibria can be greater than exponential in the size of the strategy spaces. In polynomial games there can exist extreme correlated equilibria which are not finitely supported; we construct a large family of examples using techniques from ergodic theory. We show that in general the set of correlated equilibrium distributions of a polynomial game cannot be described by conditions on finitely many moments (means, covariances, etc.), in marked contrast to the set of Nash equilibria which is always expressible in terms of finitely many moments.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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DOI of Published Version
https://doi.org/10.1007/s00182-010-0267-1
