Correlation and common priors in games with incomplete information

This paper provides an explicit characterization of correlations that are implicitly captured by partition models for incomplete information games. The main result of this paper shows that every partition model for incomplete information can be decomposed into the conjunctions of a unique non-redundant model and a unique “individually uninformative” correlating device. The separation of the correlating device from the underlying non-redundant model allows us to separate their strategic implications. As an application, we use this correlation device to define correlated equilibria. Separating the common-prior property of the correlating devices from the underlying state space sheds light on the difference between interim independent and correlated rationalizability.