## Seminar in Microeconomics - Christian W. Bach (University of Liverpool & EPICENTER Maastricht)

**Two Definitions of Correlated Equilibrium**

### Wednesday 15 May 2019 (11h00 - 12h30) - Extranef - 109

Correlated equilibrium constitutes one of the basic solution concepts for static games with complete information. Actually two variants of correlated equilibrium are in circulation and have been used interchangeably in the literature. Besides the original notion due to Aumann (1974), there exists a simplified definition typically called canonical correlated equilibrium or correlated equilibrium distribution. We show that the original and the canonical versions of correlated equilibrium are fundamentally distinct. Indeed, neither doxastically nor behaviourally they are equivalent. While Aumann's correlated equilibrium can be epistemically characterized by common belief in rationality and a common prior, canonical correlated equilibrium additionally requires the substantial assumption of one-theory-per-choice. Since this assumption features a correctness of beliefs property, the latter solution concept exhibits a larger degree of Nash equilibrium flavour than the former. Thus, the application of correlated equilibrium requires a careful choice of the appropriate version.

**Published 18 February 2019**

Joao Montez