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The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency

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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 characterized and shown to be equivalent to the set of a version of incomplete information correlated equilibria which we dub Bayes correlated equilibria. A game of incomplete information can be decomposed into a basic game, given by actions sets and payoff functions, and an information structure. We introduce a partial order on many player information structures -- which we call individual sufficiency -- under which more information shrinks the set of Bayes correlated equilibria. We discuss the relation of the solution concept to alternative definitions of correlated equilibrium in incomplete information games and of the partial order on information structures to others, including Blackwell's for the single player case.

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  • 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.
  • Handle: RePEc:cwl:cwldpp:1909r
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    8. 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).
    9. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
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    11. 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.
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    Cited by:

    1. Bernard Herskovic & João Ramos, 2020. "Acquiring Information through Peers," American Economic Review, American Economic Association, vol. 110(7), pages 2128-2152, July.
    2. Bergemann, Dirk & Heumann, Tibor & Morris, Stephen, 2015. "Information and volatility," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 427-465.
    3. 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.
    4. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    5. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    6. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.

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    More about this item

    Keywords

    Correlated equilibrium; Incomplete information; Robust predictions; Information structure; Sufficiency; 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

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