Two definitions of correlated equilibrium

Christian W. Bach*, Andres Perea

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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. (c) 2020 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)12-24
Number of pages13
JournalJournal of Mathematical Economics
Publication statusPublished - Oct 2020


  • Canonical correlated equilibrium
  • Correlated equilibrium
  • Correlated equilibrium distribution
  • Epistemic game theory
  • One-theory-per-choice condition
  • Revelation principle

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