IDEAS home Printed from https://ideas.repec.org/p/pri/metric/054-2013.html
   My bibliography  Save this paper

Bayes Correlated Equilibrium and the Comparison of Information Structures in Games

Author

Listed:
  • Dirk Bergemann

    (Yale University)

  • Stephen Morris

    (Princeton University)

Abstract

The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the given information structure is equivalent to the set of a version of incomplete information correlated equilibrium which we dub Bayes correlated equilibrium. A game of incomplete information can be decomposed into a basic game, given by actions sets and payoff functions, and an information structure. We identify a partial order on many player information structures (individual sufficiency) under which more information shrinks the set of Bayes correlated equilibria.

Suggested Citation

  • Dirk Bergemann & Stephen Morris, 2013. "Bayes Correlated Equilibrium and the Comparison of Information Structures in Games," Working Papers 054-2013, Princeton University, Department of Economics, Econometric Research Program..
    • Handle: RePEc:pri:metric:054-2013
    as

    Download full text from publisher

    File URL: http://detc.princeton.edu/wp-content/uploads/2016/11/wp054_2013-revised-19Oct14_Bergemann_Morris_The-Comparison-of-Information-Structures-in-Games.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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, 2015. "The Limits of Price Discrimination," American Economic Review, American Economic Association, vol. 105(3), pages 921-957, March.
    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    4. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    5. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
    6. Dirk Bergemann & Stephen Morris, 2011. "Correlated Equilibrium in Games with Incomplete Information," Cowles Foundation Discussion Papers 1822, Cowles Foundation for Research in Economics, Yale University.
    7. Ina Taneva, 2019. "Information Design," American Economic Journal: Microeconomics, American Economic Association, vol. 11(4), pages 151-185, November.
    8. Dirk Bergemann & Stephen Morris, 2013. "The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency," Levine's Working Paper Archive 786969000000000730, David K. Levine.
    9. 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..
    10. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation for Research in Economics, Yale University.
    11. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    12. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    13. Gossner, Olivier, 2010. "Ability and knowledge," Games and Economic Behavior, Elsevier, vol. 69(1), pages 95-106, May.
    14. Bergemann, Dirk & Heumann, Tibor & Morris, Stephen, 2015. "Information and volatility," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 427-465.
    15. 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.
    16. Andrew Caplin & Daniel Martin, 2015. "A Testable Theory of Imperfect Perception," Economic Journal, Royal Economic Society, vol. 125(582), pages 184-202, February.
    17. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," LIDAM Discussion Papers CORE 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. 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.
    19. repec:dau:papers:123456789/157 is not listed on IDEAS
    20. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    21. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    22. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    23. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    24. Peski, Marcin, 2008. "Comparison of information structures in zero-sum games," Games and Economic Behavior, Elsevier, vol. 62(2), pages 732-735, March.
    25. Olivier Gossner, 2010. "Ability and Knowledge," PSE-Ecole d'économie de Paris (Postprint) halshs-00754449, HAL.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    2. Dirk Bergemann & Stephen Morris, 2013. "The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency," Cowles Foundation Discussion Papers 1909R, Cowles Foundation for Research in Economics, Yale University, revised May 2014.
    3. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    4. Tang, Qianfeng, 2015. "Interim partially correlated rationalizability," Games and Economic Behavior, Elsevier, vol. 91(C), pages 36-44.
    5. Dirk Bergemann & Stephen Morris, 2013. "Bayes Correlated Equilibrium and the Comparison of Information Structures," Levine's Working Paper Archive 786969000000000725, David K. Levine.
    6. Cédric Wanko, 2018. "A Unique and Stable $$\hbox {Se}{\mathcal {C}}\hbox {ure}$$ Se C ure Reversion Protocol Improving Efficiency: A Computational Bayesian Approach for Empirical Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 1-23, June.
    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. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    9. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    10. Tang, Qianfeng, 2015. "Hierarchies of beliefs and the belief-invariant Bayesian solution," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 111-116.
    11. Dirk Bergemann & Stephen Morris, 2011. "Correlated Equilibrium in Games with Incomplete Information," Levine's Working Paper Archive 786969000000000265, David K. Levine.
    12. 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.
    13. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    14. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    15. 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.
    16. Takashi Ui & Stephen Morris, 2020. "Incomplete Information Robustness," Working Papers on Central Bank Communication 019, University of Tokyo, Graduate School of Economics.
    17. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    18. Dughmi, Shaddin, 2019. "On the hardness of designing public signals," Games and Economic Behavior, Elsevier, vol. 118(C), pages 609-625.
    19. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2015. "The Limits of Price Discrimination," American Economic Review, American Economic Association, vol. 105(3), pages 921-957, March.
    20. Dirk Bergemann & Stephen Morris, 2014. "Informational Robustness and Solution Concepts," Cowles Foundation Discussion Papers 1973, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    Keywords

    Correlated equilibrium; incomplete information; robust predictions; information structure; su¢ ciency; Blackwell ordering;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pri:metric:054-2013. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bobray Bordelon (email available below). General contact details of provider: https://edirc.repec.org/data/exprius.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.