We analyze games of incomplete information and oﬀer equilibrium predictions which are valid for all possible private information structures that the agents may have. Our characterization of these robust predictions relies on an epistemic result which establishes a relationship between the set of Bayes Nash equilibria and the set of Bayes correlated equilibria. We completely characterize the set of Bayes correlated equilibria in a class of games with quadratic payoﬀs and normally distributed uncertainty in terms of restrictions on the ﬁrst and second moments of the equilibrium action-state distribution. We derive exact bounds on how prior information of the analyst reﬁnes the set of equilibrium distribution. As an application, we obtain new results regarding the optimal information sharing policy of ﬁrms under demand uncertainty. Finally, we reverse the perspective and investigate the identiﬁcation problem under concerns for robustness to private information. We show how the presence of private information leads to partial rather than complete identiﬁcation of the structural parameters of the game. As a prominent example we analyze the canonical problem of demand and supply identiﬁcation.
Bergemann, Dirk and Morris, Stephen, "Robust Predictions in Games with Incomplete Information" (2011). Cowles Foundation Discussion Papers. 2169.