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Feasible Joint Posterior Beliefs

Author

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  • Itai Arieli
  • Yakov Babichenko
  • Fedor Sandomirskiy
  • Omer Tamuz

Abstract

We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state, and who observe some information structure. For two agents we introduce a quantitative version of Aumann's Agreement Theorem, and show that it is equivalent to a characterization of feasible distributions due to Dawid et al. (1995). For any number of agents, we characterize feasible distributions in terms of a "no-trade" condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.

Suggested Citation

  • Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy & Omer Tamuz, 2020. "Feasible Joint Posterior Beliefs," Papers 2002.11362, arXiv.org, revised Dec 2020.
    • Handle: RePEc:arx:papers:2002.11362
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    References listed on IDEAS

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    1. Sergiu Hart & Philip J. Reny, 2015. "Implementation of reduced form mechanisms: a simple approach and a new characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 1-8, April.
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    8. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    9. Weinstein, Jonathan & Yildiz, Muhamet, 2007. "Impact of higher-order uncertainty," Games and Economic Behavior, Elsevier, vol. 60(1), pages 200-212, July.
    10. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
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    12. Neeman, Zvika, 1996. "Approximating Agreeing to Disagree Results with Commonp-Beliefs," Games and Economic Behavior, Elsevier, vol. 12(1), pages 162-164, January.
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    Cited by:

    1. Levy, Gilat & Moreno de Barreda, Inés & Razin, Ronny, 2022. "Persuasion with correlation neglect: a full manipulation result," LSE Research Online Documents on Economics 111551, London School of Economics and Political Science, LSE Library.
    2. Kevin He & Fedor Sandomirskiy & Omer Tamuz, 2021. "Private Private Information," Papers 2112.14356, arXiv.org, revised Jun 2023.
    3. Herings, P. Jean-Jacques & Karos, Dominik & Kerman, Toygar, 2020. "Belief Inducibility and Informativeness," Research Memorandum 027, Maastricht University, Graduate School of Business and Economics (GSBE).

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