Structure of extreme correlated equilibria: a zero-sum example and its implications

被引:0
|
作者
Stein, Noah D. [1 ]
Ozdaglar, Asuman [1 ]
Parrilo, Pablo A. [1 ]
机构
[1] MIT, Dept Elect Engn, Cambridge, MA 02139 USA
基金
美国国家科学基金会;
关键词
Correlated equilibria; Extreme points; Polynomial games; Ergodic theory; NASH EQUILIBRIA; EXISTENCE;
D O I
10.1007/s00182-010-0267-1
中图分类号
F [经济];
学科分类号
02 ;
摘要
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.
引用
收藏
页码:749 / 767
页数:19
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