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Bayes Correlated Equilibrium and the Comparison of Information Structures in Games

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  • Dirk Bergemann
  • Stephen Morris

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.
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Suggested Citation

  • Dirk Bergemann & Stephen Morris, 2015. "Bayes Correlated Equilibrium and the Comparison of Information Structures in Games," Levine's Bibliography 786969000000001085, UCLA Department of Economics.
  • Handle: RePEc:cla:levrem:786969000000001085
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    References listed on IDEAS

    as
    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. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    3. 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.
    4. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476.
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    7. 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.
    8. Ina Taneva, 2019. "Information Design," American Economic Journal: Microeconomics, American Economic Association, vol. 11(4), pages 151-185, November.
    9. 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.
    10. 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..
    11. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    12. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    13. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    14. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    15. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
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    22. repec:dau:papers:123456789/157 is not listed on IDEAS
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    Full references (including those not matched with items on IDEAS)

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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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