Two definitions of correlated equilibrium

Bach, C. W. ORCID: https://orcid.org/0000-0003-0187-1820 and Perea, A. (2020) Two definitions of correlated equilibrium. Journal of Mathematical Economics, 90. pp. 12-24. ISSN 1873-1538 doi: 10.1016/j.jmateco.2020.05.001

Abstract/Summary

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. It is known that the original and the canonical version of correlated equilibrium are equivalent from an ex-ante perspective. However, we show that they are actually distinct – both doxastically as well as behaviourally – from an interim perspective. An elucidation of this difference emerges in the reasoning realm: while Aumann’s correlated equilibrium can be epistemically characterized by common belief in rationality and a common prior, canonical correlated equilibrium additionally requires the condition of one-theory-per-choice. Consequently, the application of correlated equilibrium requires a careful choice of the appropriate variant.