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Robust Predictions in Games with Incomplete Information

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.

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File URL: http://cowles.econ.yale.edu/P/cd/d18a/d1821-rr.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1821RR.

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Length: 54 pages
Date of creation: Sep 2011
Date of revision: Oct 2012
Handle: RePEc:cwl:cwldpp:1821rr
Contact details of provider: Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Bergemann, Dirk & Pesendorfer, Martin, 2001. "Information Structures in Optimal Auctions," CEPR Discussion Papers 2991, C.E.P.R. Discussion Papers.
  2. Vives, Xavier, 1984. "Duopoly information equilibrium: Cournot and bertrand," Journal of Economic Theory, Elsevier, vol. 34(1), pages 71-94, October.
  3. Atsushi Kajii & Stephen Morris, . ""The Robustness of Equilibria to Incomplete Information*''," CARESS Working Papres 95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  4. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, 03.
  5. Dirk Bergemann & Stephen Morris & Satoru Takahashi, 2010. "Interdependent Preferences and Strategic Distinguishability," Cowles Foundation Discussion Papers 1772R, Cowles Foundation for Research in Economics, Yale University, revised Feb 2011.
  6. FORGES, Françoise, 2006. "Correlated equilibrium in games with incomplete information revisited," CORE Discussion Papers 2006041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Coralio Ballester & Antoni Calvo-Armengol & Yves Zenou, 2005. "Who's Who in Networks. Wanted: the Key Player," NajEcon Working Paper Reviews 666156000000000586, www.najecon.org.
  8. Xun Tang & Aureo de Paula, 2010. "Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information," 2010 Meeting Papers 1087, Society for Economic Dynamics.
  9. Dirk Bergemann & Juuso Vaimaki, 2000. "Information Acquisition and Efficient Mechanism Design," Cowles Foundation Discussion Papers 1248, Cowles Foundation for Research in Economics, Yale University.
  10. David Brillinger, 1969. "The calculation of cumulants via conditioning," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 215-218, December.
  11. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
  12. Emir Kamenica & Matthew Gentzkow, 2009. "Bayesian Persuasion," NajEcon Working Paper Reviews 814577000000000369, www.najecon.org.
  13. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer, vol. 26(2), pages 223-227.
  14. Patrick Bajari & Han Hong & John Krainer & Denis Nekipelov, 2006. "Estimating Static Models of Strategic Interaction," NBER Working Papers 12013, National Bureau of Economic Research, Inc.
  15. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," CORE Discussion Papers 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. George-Marios Angeletos & Alessandro Pavan, 2007. "Efficient Use of Information and Social Value of Information," Econometrica, Econometric Society, vol. 75(4), pages 1103-1142, 07.
  17. Aradillas-Lopez, Andres & Tamer, Elie, 2008. "The Identification Power of Equilibrium in Simple Games," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 261-310.
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