The correlated equilibrium is a game theoretic solution concept. It was
proposed by Aumann (1974, 1987) in order to capture the strategic corre-
lation opportunities that the players face when they take into account the
extraneous environment in which they interact. The notion is illustrated in
Section II. A formal definition is given in Section III. The correlated equilibrium also appears as the appropriate solution concept if preplay communi-
cation is allowed between the players. As shown in Section IV, this property
can be given several precise statements according to the constraints imposed
on the playersícommunication, which can go from plain conversation to ex-
change of messages through noisy channels. Originally designed for static games with complete information, the correlated equilibrium applies to any
strategic form game. It is geometrically and computationally more tractable
than the better known Nash equilibrium. The solution concept has been
extended to dynamic games, possibly with incomplete information. As an
illustration, we define in details the communication equilibrium for Bayesian
games in Section V.
