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Bayes Correlated Equilibrium and the Comparison of Information Structures in Games

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Abstract

A game of incomplete information can be decomposed into a basic game and an information structure. The basic game defines the set of actions, the set of payoff states the payoff functions and the common prior over the payoff states. The information structure refers to the signals that the players receive in the game. We characterize the set of outcomes that can arise in Bayes Nash equilibrium if players observe the given information structure but may also observe additional signals. The characterization corresponds to the set of (a version of) incomplete information correlated equilibria which we dub Bayes correlated equilibria. We identify a partial order on many player information structures (individual sufficiency) under which more information shrinks the set of Bayes correlated equilibria. This order captures the role of information in imposing (incentive) constraints on behavior.

Suggested Citation

  • Dirk Bergemann & Stephen Morris, 2013. "Bayes Correlated Equilibrium and the Comparison of Information Structures in Games," Cowles Foundation Discussion Papers 1909R3, Cowles Foundation for Research in Economics, Yale University, revised Apr 2015.
  • Handle: RePEc:cwl:cwldpp:1909rrr
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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.
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    Citations

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    Cited by:

    1. Dirk Bergemann & Stephen Morris, 2016. "Information Design, Bayesian Persuasion, and Bayes Correlated Equilibrium," American Economic Review, American Economic Association, vol. 106(5), pages 586-591, May.
    2. Ryan Chahrour & Robert Ulbricht, 2017. "Information-driven Business Cycles: A Primal Approach," Boston College Working Papers in Economics 925, Boston College Department of Economics.
    3. Vladimir Asriyan & William Fuchs & Brett Green, 2017. "Information aggregation in dynamic markets with adverse selection," Economics Working Papers 1573, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2017.
    4. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    5. 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.
    6. Tang, Qianfeng, 2015. "Hierarchies of beliefs and the belief-invariant Bayesian solution," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 111-116.
    7. Alonso, Ricardo & Câmara, Odilon, 2018. "On the value of persuasion by experts," Journal of Economic Theory, Elsevier, vol. 174(C), pages 103-123.
    8. repec:kap:compec:v:52:y:2018:i:1:d:10.1007_s10614-017-9646-z is not listed on IDEAS
    9. Vasilis Syrgkanis & Elie Tamer & Juba Ziani, 2017. "Inference on Auctions with Weak Assumptions on Information," Papers 1710.03830, arXiv.org, revised Mar 2018.
    10. Dirk Bergemann & Tibor Heumann & Stephen Morris, 2015. "Information and Market Power," Levine's Bibliography 786969000000001101, UCLA Department of Economics.
    11. repec:eee:gamebe:v:109:y:2018:i:c:p:126-131 is not listed on IDEAS
    12. E. Carroni & L. Ferrari & S. Righi, 2018. "The Price of Discovering Your Needs Online," Working Papers wp1116, Dipartimento Scienze Economiche, Universita' di Bologna.
    13. Tang, Qianfeng, 2015. "Interim partially correlated rationalizability," Games and Economic Behavior, Elsevier, vol. 91(C), pages 36-44.
    14. Carroll, Gabriel, 2016. "Informationally robust trade and limits to contagion," Journal of Economic Theory, Elsevier, vol. 166(C), pages 334-361.
    15. Pavan, Alessandro & Vives, Xavier, 2015. "Information, Coordination, and Market Frictions: An Introduction," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 407-426.
    16. Kloosterman, Andrew, 2015. "Public information in Markov games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 28-48.
    17. Elias Tsakas & Nikolas Tsakas, 2018. "Noisy Persuasion," University of Cyprus Working Papers in Economics 11-2018, University of Cyprus Department of Economics.
    18. Daniel Kraehmer, 2018. "Full surplus extraction in mechanism design with information disclosure," CRC TR 224 Discussion Paper Series crctr224_011_2018, University of Bonn and University of Mannheim, Germany.

    More about this item

    Keywords

    Correlated equilibrium; Incomplete information; Bayes Nash equilibrium; Bayes correlated equilibrium; Robust predictions; Information structure; Sufficiency; Blackwell ordering;

    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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