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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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  • 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. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
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    11. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    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.
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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. 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. 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.
    5. Blume, Andreas, 2012. "A class of strategy-correlated equilibria in sender–receiver games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 510-517.
    6. 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.
    7. 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.
    8. Yang, Jianxia & Wu, John, 2013. "Strategic correlativity and network games," Economic Modelling, Elsevier, vol. 30(C), pages 663-669.
    9. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.

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    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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