We deﬁne a notion of correlated equilibrium for games with incomplete information in a general setting with ﬁnite players, ﬁnite actions, and ﬁnite states, which we call Bayes correlated equilibrium. The set of Bayes correlated equilibria of a ﬁxed incomplete information game equals the set of probability distributions over actions, states and types that might arise in any Bayes Nash equilibrium where players observed additional information. We show that more information always shrinks the set of Bayes correlated equilibria.
Bergemann, Dirk and Morris, Stephen, "Correlated Equilibrium in Games with Incomplete Information" (2011). Cowles Foundation Discussion Papers. 2173.