We acknowledge financial support through NSF Grant SES 0851200. The present paper formed the basis of the Fisher–Schultz Lecture given by Stephen Morris at the 2012 European Meeting of the Econometric Society in Malaga. We would like to thank a co-editor and two anonymous referees for their detailed comments. We benefitted from conversations with Steve Berry, Vincent Crawford, Matthew Gentzkow, Phil Haile, Emir Kamenica, Marc Henry, Arthur Lewbel, Larry Samuelson, Elie Tamer, Takashi Ui, and Xavier Vives, as well as research assistance from Brian Baisa, Constantinos Kalfarentzos, and Aron Tobias. We would like to thank seminar audiences at Boston College, the Collegio Carlo Alberto, École Polytechnique, European University Institute, HEC, Microsoft Research, Northwestern University, the Paris School of Economics, Stanford University, and the University of Colorado for stimulating conversations, and we thank David McAdams for his discussion at the 2011 North American Winter Meetings of the Econometric Society.
Robust Predictions in Games With Incomplete Information
Article first published online: 26 JUL 2013
© 2013 The Econometric Society
Volume 81, Issue 4, pages 1251–1308, July 2013
How to Cite
Bergemann, D. and Morris, S. (2013), Robust Predictions in Games With Incomplete Information. Econometrica, 81: 1251–1308. doi: 10.3982/ECTA11105
- Issue published online: 26 JUL 2013
- Article first published online: 26 JUL 2013
- Manuscript received September, 2012; final revision received March, 2013.
- Incomplete information;
- correlated equilibrium;
- robustness to private information;
- moment restrictions;
- information bounds;
- linear best responses;
- quadratic payoffs
We analyze games of incomplete information and offer equilibrium predictions that 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.