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Correlated Equilibrium in Games with Incomplete Information

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  • Dirk Bergemann
  • Stephen Morris

Abstract

We define a notion of correlated equilibrium for games with incomplete information in a general setting with finite players, finite actions, and finite states, which we call Bayes correlated equilibrium. The set of Bayes correlated equilibria of a fixed incomplete information game equals the set of probability distributions over actions, states and types that might arise in any Bayes Nash equilibrium where players observed additional information. We show that more information always shrinks the set of Bayes correlated equilibria.
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Suggested Citation

  • Dirk Bergemann & Stephen Morris, 2011. "Correlated Equilibrium in Games with Incomplete Information," Levine's Working Paper Archive 786969000000000265, David K. Levine.
  • Handle: RePEc:cla:levarc:786969000000000265
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    References listed on IDEAS

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    1. Andrew Caplin & Daniel Martin, 2015. "A Testable Theory of Imperfect Perception," Economic Journal, Royal Economic Society, vol. 125(582), pages 184-202, February.
    2. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    3. Forges, Francoise & Koessler, Frederic, 2005. "Communication equilibria with partially verifiable types," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 793-811, November.
    4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    5. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June.
    6. 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.
    7. Robert F. Nau, 1992. "Joint Coherence in Games of Incomplete Information," Management Science, INFORMS, vol. 38(3), pages 374-387, March.
    8. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    9. Ely, Jeffrey C. & Peski, Marcin, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    10. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    11. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation for Research in Economics, Yale University.
    12. repec:dau:papers:123456789/168 is not listed on IDEAS
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    Cited by:

    1. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    2. Blume, Andreas, 2012. "A class of strategy-correlated equilibria in sender–receiver games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 510-517.
    3. Benhabib, Jess & Liu, Xuewen & Wang, Pengfei, 2016. "Sentiments, financial markets, and macroeconomic fluctuations," Journal of Financial Economics, Elsevier, vol. 120(2), pages 420-443.
    4. Yang, Jianxia & Wu, John, 2013. "Strategic correlativity and network games," Economic Modelling, Elsevier, vol. 30(C), pages 663-669.
    5. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

    More about this item

    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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