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Bayes Correlated Equilibrium and the Comparison of Information Structures

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The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may or may not have access to more private information is characterized and shown to be equivalent to the set of an incomplete information version of correlated equilibrium, which we call Bayes correlated equilibrium. We describe a partial order on many player information structures -- which we call individual sufficiency -- under which more information shrinks the set of Bayes correlated equilibria. We discuss the relation of the solution concept to alternative definitions of correlated equilibrium in incomplete information games and of the partial order on information structures to others, including Blackwell's for the single player case.

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  • Dirk Bergemann & Stephen Morris, 2013. "Bayes Correlated Equilibrium and the Comparison of Information Structures," Cowles Foundation Discussion Papers 1822R, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1822r
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    1. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    2. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2013. "Extremal Information Structures in the First Price Auction," Working Papers 055-2013, Princeton University, Department of Economics, Econometric Research Program..
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    5. Andrew Caplin & Daniel Martin, 2015. "A Testable Theory of Imperfect Perception," Economic Journal, Royal Economic Society, vol. 125(582), pages 184-202, February.
    6. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    7. Hirshleifer, Jack, 1971. "The Private and Social Value of Information and the Reward to Inventive Activity," American Economic Review, American Economic Association, vol. 61(4), pages 561-574, September.
    8. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June.
    9. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
    10. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2010. "Signaling and mediation in games with common interests," Games and Economic Behavior, Elsevier, vol. 68(2), pages 670-682, March.
    11. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    12. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation for Research in Economics, Yale University.
    13. Forges, Francoise & Koessler, Frederic, 2005. "Communication equilibria with partially verifiable types," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 793-811, November.
    14. Robert F. Nau, 1992. "Joint Coherence in Games of Incomplete Information," Management Science, INFORMS, vol. 38(3), pages 374-387, March.
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    Cited by:

    1. Alejandro Melo Ponce, 2018. "The Secret Behind The Tortoise and the Hare: Information Design in Contests," 2018 Papers pme809, Job Market Papers.
    2. Taneva, Ina A, 2015. "Information Design," SIRE Discussion Papers 2015-50, Scottish Institute for Research in Economics (SIRE).
    3. Zhen Zhou & Deepal Basak, 2015. "Diffusing Coordination Risk," 2015 Meeting Papers 1350, Society for Economic Dynamics.
    4. Andrew Caplin & Mark Dean, 2015. "Revealed Preference, Rational Inattention, and Costly Information Acquisition," American Economic Review, American Economic Association, vol. 105(7), pages 2183-2203, July.
    5. Taneva, Ina A, 2015. "Information Design," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-50, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    6. Kloosterman, Andrew, 2015. "Public information in Markov games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 28-48.
    7. Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.
    8. Ina Taneva, 2019. "Information Design," American Economic Journal: Microeconomics, American Economic Association, vol. 11(4), pages 151-185, November.
    9. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    10. Gregory Pavlov, 2013. "Correlated Equilibria and Communication Equilibria in All-pay Auctions," University of Western Ontario, Departmental Research Report Series 20132, University of Western Ontario, Department of Economics.
    11. Caplin, Andrew, 2014. "Rational inattention and revealed preference: The data-theoretic approach to economic modeling," Research in Economics, Elsevier, vol. 68(4), pages 295-305.

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    More about this item

    Keywords

    Correlated equilibrium; Incomplete information; Robust predictions; Information structure;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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