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Robust Predictions in Games with Incomplete Information

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  • Dirk Bergemann
  • Stephen Morris

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.

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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

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  1. Bergemann, Dirk & Pesendorfer, Martin, 2001. "Information Structures in Optimal Auctions," CEPR Discussion Papers, C.E.P.R. Discussion Papers 2991, C.E.P.R. Discussion Papers.
  2. Dirk Bergemann & Stephen Morris & Satoru Takahashi, 2011. "Interdependent Preferences and Strategic Distinguishability," Levine's Working Paper Archive 786969000000000054, David K. Levine.
  3. Emir Kamenica & Matthew Gentzkow, 2009. "Bayesian Persuasion," NajEcon Working Paper Reviews, www.najecon.org 814577000000000369, www.najecon.org.
  4. 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.
  5. Abraham Neyman, 1997. "Correlated Equilibrium and Potential Games," International Journal of Game Theory, Springer, Springer, vol. 26(2), pages 223-227.
  6. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, American Economic Association, vol. 79(3), pages 385-91, June.
  7. Xun Tang & Aureo de Paula, 2010. "Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information," 2010 Meeting Papers, Society for Economic Dynamics 1087, Society for Economic Dynamics.
  8. Bajari, Patrick & Hong, Han & Krainer, John & Nekipelov, Denis, 2010. "Estimating Static Models of Strategic Interactions," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 28(4), pages 469-482.
  9. repec:wop:humbsf:2000-72 is not listed on IDEAS
  10. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1283-1310, November.
  11. Vives, Xavier, 1984. "Duopoly information equilibrium: Cournot and bertrand," Journal of Economic Theory, Elsevier, Elsevier, vol. 34(1), pages 71-94, October.
  12. FORGES, Françoise, . "Five legitimate definitions of correlated equilibrium in games with incomplete informations," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1071, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Aradillas-Lopez, Andres & Tamer, Elie, 2008. "The Identification Power of Equilibrium in Simple Games," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 26, pages 261-310.
  14. Dirk Bergemann & Juuso Vaimaki, 2000. "Information Acquisition and Efficient Mechanism Design," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1248, Cowles Foundation for Research in Economics, Yale University.
  15. David Brillinger, 1969. "The calculation of cumulants via conditioning," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 21(1), pages 215-218, December.
  16. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, Econometric Society, vol. 75(2), pages 365-400, 03.
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Cited by:
  1. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, Elsevier, vol. 81(C), pages 179-191.

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