Robust Predictions in Games with Incomplete Information

64 Pages Posted: 27 Sep 2011  

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics; Yale University - Cowles Foundation

Stephen Morris

Princeton University - Department of Economics

Multiple version iconThere are 4 versions of this paper

Date Written: September 26, 2011

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 restrictions, Identification, Information bounds

JEL Classification: C72, C73, D43, D83

Suggested Citation

Bergemann, Dirk and Morris, Stephen, Robust Predictions in Games with Incomplete Information (September 26, 2011). Cowles Foundation Discussion Paper No. 1821; Economic Theory Center Working Paper No. 023-2011. Available at SSRN: https://ssrn.com/abstract=1933781 or http://dx.doi.org/10.2139/ssrn.1933781

Dirk Bergemann (Contact Author)

Yale University - Cowles Foundation - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3592 (Phone)
203-432-2128 (Fax)

HOME PAGE: http://www.econ.yale.edu/~dirk/

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Stephen Edward Morris

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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