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We analyze games of incomplete information and oﬀer equilibrium predictions which are valid for, and in this sense robust to, all possible private information structures that the agents may have. 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 knowledge about the private information reﬁnes the set of equilibrium predictions. We consider information sharing among ﬁrms under demand uncertainty and ﬁnd newly optimal information policies via the Bayes correlated equilibria. Finally, we reverse the perspective and investigate the identiﬁcation problem under concerns for robustness to private information. The presence of private information leads to set rather than point identiﬁcation of the structural parameters of the game.
Bergemann, Dirk and Morris, Stephen, "Robust Predictions in Games with Incomplete Information" (2011). Cowles Foundation Discussion Papers. 2170.