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Robust Predictions in Games with Incomplete Information

  • Dirk Bergemann
  • Stephen Morris

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.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000275.

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Date of creation: 20 Oct 2011
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Handle: RePEc:cla:levarc:786969000000000275
Contact details of provider: Web page: http://www.dklevine.com/

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  1. FORGES, Françoise, . "Five legitimate definitions of correlated equilibrium in games with incomplete informations," CORE Discussion Papers RP -1071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Emir Kamenica & Matthew Gentzkow, 2009. "Bayesian Persuasion," NBER Working Papers 15540, National Bureau of Economic Research, Inc.
  3. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2004. "Who's Who in Networks. Wanted: The Key Player," Working Papers 178, Barcelona Graduate School of Economics.
  4. Dirk Bergemann & Juuso Vaimaki, 2000. "Information Acquisition and Efficient Mechanism Design," Cowles Foundation Discussion Papers 1248, Cowles Foundation for Research in Economics, Yale University.
  5. Dirk Bergemann & Martin Pesendorfer, 2001. "Information Structures in Optimal Auctions," Cowles Foundation Discussion Papers 1323, Cowles Foundation for Research in Economics, Yale University.
  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. Vives, Xavier, 1984. "Duopoly information equilibrium: Cournot and bertrand," Journal of Economic Theory, Elsevier, vol. 34(1), pages 71-94, October.
  8. Aureo de Paula & Xun Tang, 2010. "Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information," PIER Working Paper Archive 10-010, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  9. David Brillinger, 1969. "The calculation of cumulants via conditioning," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 215-218, December.
  10. Bajari, Patrick & Hong, Han & Krainer, John & Nekipelov, Denis, 2010. "Estimating Static Models of Strategic Interactions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 469-482.
  11. 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.
  12. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
  13. Dirk Bergemann & Stephen Morris & Satoru Takahashi, 2010. "Interdependent Preferences and Strategic Distinguishability," Levine's Working Paper Archive 661465000000000273, David K. Levine.
  14. 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.
  15. 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.
  16. 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.
  17. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer, vol. 26(2), pages 223-227.
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