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A population's feasible posterior beliefs

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Listed:
  • Arieli, Itai
  • Babichenko, Yakov

Abstract

We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We characterize which distributions over the empirical distribution of posterior beliefs in the population are feasible. We apply this result in several domains. First, we study the problem of maximizing the polarization of beliefs in a population. Second, we provide a characterization of the feasible agent-symmetric product distributions of posteriors. Finally, we study an instance of a private Bayesian persuasion problem and provide a clean formula for the sender's optimal value.

Suggested Citation

  • Arieli, Itai & Babichenko, Yakov, 2024. "A population's feasible posterior beliefs," Journal of Economic Theory, Elsevier, vol. 215(C).
    • Handle: RePEc:eee:jetheo:v:215:y:2024:i:c:s0022053123001606
    DOI: 10.1016/j.jet.2023.105764
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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.
    2. Eran Shmaya & Leeat Yariv, 2016. "Experiments on Decisions under Uncertainty: A Theoretical Framework," American Economic Review, American Economic Association, vol. 106(7), pages 1775-1801, July.
    3. A. Dawid & M. DeGroot & J. Mortera & R. Cooke & S. French & C. Genest & M. Schervish & D. Lindley & K. McConway & R. Winkler, 1995. "Coherent combination of experts' opinions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(2), pages 263-313, December.
    4. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy & Omer Tamuz, 2021. "Feasible Joint Posterior Beliefs," Journal of Political Economy, University of Chicago Press, vol. 129(9), pages 2546-2594.
    5. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
    6. Arieli, Itai & Babichenko, Yakov, 2019. "Private Bayesian persuasion," Journal of Economic Theory, Elsevier, vol. 182(C), pages 185-217.
    7. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
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    Cited by:

    1. Stanisław Cichomski & Adam Osȩkowski, 2025. "On the Existence of Extreme Coherent Distributions with No Atoms," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-15, March.

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    More about this item

    Keywords

    Feasible posterior distribution; Empirical distributions of posteriors; Polarization; Bayesian persuasion;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • 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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