Robust Predictions in Games with Incomplete Information

Bergemann, Dirk; Morris, Stephen

Robust Predictions in Games with Incomplete Information

No 1356, Working Papers from Princeton University, Department of Economics, Econometric Research Program.

Abstract: 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.

Keywords: Incomplete Information; Correlated Equilibrium; Robustness to Private Information; Moments Re- strictions; Identi?cation; Information Bounds (search for similar items in EconPapers)
JEL-codes: C72 C73 D43 D83 (search for similar items in EconPapers)
Date: 2011-09
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