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Correlated Equilibrium in Games with Incomplete Information

Author

Listed:
  • Dirk Bergemann

    (Yale University)

  • Stephen Morris

    (Princeton University)

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.

Suggested Citation

  • Dirk Bergemann & Stephen Morris, 2011. "Correlated Equilibrium in Games with Incomplete Information," Working Papers 1358, Princeton University, Department of Economics, Econometric Research Program..
    • Handle: RePEc:pri:metric:024_2011
    as

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    References listed on IDEAS

    as
    1. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    2. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    3. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation for Research in Economics, Yale University.
    4. Robert J. Aumann & Jacques H. Dreze, 2008. "Rational Expectations in Games," American Economic Review, American Economic Association, vol. 98(1), pages 72-86, March.
    5. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    6. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    7. Forges, Francoise & Koessler, Frederic, 2005. "Communication equilibria with partially verifiable types," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 793-811, November.
    8. 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.
    9. Andrew Caplin & Daniel Martin, 2015. "A Testable Theory of Imperfect Perception," Economic Journal, Royal Economic Society, vol. 125(582), pages 184-202, February.
    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. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June.
    12. Robert F. Nau, 1992. "Joint Coherence in Games of Incomplete Information," Management Science, INFORMS, vol. 38(3), pages 374-387, March.
    13. repec:dau:papers:123456789/168 is not listed on IDEAS
    14. Tang, Qianfeng, 2010. "The Bayesian Solution and Hierarchies of Beliefs," MPRA Paper 26811, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jess Benhabib & Pengfei Wang & Yi Wen, 2017. "Uncertainty and Sentiment-Driven Equilibria," Studies in Economic Theory, in: Kazuo Nishimura & Alain Venditti & Nicholas C. Yannelis (ed.), Sunspots and Non-Linear Dynamics, chapter 0, pages 281-304, Springer.
    2. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    3. Helmuts Āzacis & Péter Vida, 2015. "Collusive communication schemes in a first-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 125-160, January.
    4. Blume, Andreas, 2012. "A class of strategy-correlated equilibria in sender–receiver games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 510-517.
    5. Zhuozheng Li & Huanxing Yang & Lan Zhang, 2019. "Pre-communication in a coordination game with incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 109-141, March.
    6. Igal Milchtaich, 2014. "Implementability of correlated and communication equilibrium outcomes in incomplete information games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 283-350, May.
    7. Yang, Jianxia & Wu, John, 2013. "Strategic correlativity and network games," Economic Modelling, Elsevier, vol. 30(C), pages 663-669.
    8. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Benhabib, Jess & Liu, Xuewen & Wang, Pengfei, 2016. "Sentiments, financial markets, and macroeconomic fluctuations," Journal of Financial Economics, Elsevier, vol. 120(2), pages 420-443.

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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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