Robust Predictions in Games with Incomplete Information

61 Pages Posted: 20 Mar 2013 Last revised: 8 May 2013

See all articles by Dirk Bergemann

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: March 31, 2013

Abstract

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. The set of outcomes that can arise in equilibrium for some information structure is equal to 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 knowledge about the private information refines the set of equilibrium predictions.

We consider information sharing among firms under demand uncertainty and find new optimal information policies via the Bayes correlated equilibria. We also 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.

Keywords: Incomplete information, Correlated equilibrium, Robustness to private information, Moments restrictions, Identification, Informations bounds, Linear best responses, Quadratic payoffs

JEL Classification: C72, C73, D43, D83

Suggested Citation

Bergemann, Dirk and Morris, Stephen Edward, Robust Predictions in Games with Incomplete Information (March 31, 2013). Cowles Foundation Discussion Paper No. 1821RRR; Economic Theory Center Working Paper No. 023-2011. Available at SSRN: https://ssrn.com/abstract=2235253 or http://dx.doi.org/10.2139/ssrn.2235253

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

Register to save articles to
your library

Register

Paper statistics

Downloads
58
Abstract Views
756
rank
42,062
PlumX Metrics