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Optimal persuasion via bi-pooling

Author

Listed:
  • Arieli, Itai

    (Technion–Israel Institute of Technology)

  • Babichenko, Yakov

    (Technion–Israel Institute of Technology)

  • Smorodinsky, Rann

    (Technion–Israel Institute of Technology)

  • Yamashita, Takuro

    (Toulouse School of Economics, University of Toulouse Capitole)

Abstract

Mean-preserving contractions are critical for studying Bayesian models of information design. We introduce the class of bi-pooling policies, and the class of bi-pooling distributions as their induced distributions over posteriors. We show that every extreme point in the set of all mean-preserving contractions of any given prior over an interval takes the form of a bi-pooling distribution. By implication, every Bayesian persuasion problem with an interval state-space admits an optimal bi-pooling distribution as a solution, and conversely, for every bi-pooling distribution, there is a Bayesian persuasion problem for which that distribution is the unique solution

Suggested Citation

  • Arieli, Itai & Babichenko, Yakov & Smorodinsky, Rann & Yamashita, Takuro, 2023. "Optimal persuasion via bi-pooling," Theoretical Economics, Econometric Society, vol. 18(1), January.
    • Handle: RePEc:the:publsh:4663
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    References listed on IDEAS

    as
    1. Anne-Katrin Roesler & Balázs Szentes, 2017. "Buyer-Optimal Learning and Monopoly Pricing," American Economic Review, American Economic Association, vol. 107(7), pages 2072-2080, July.
    2. Andreas Kleiner & Benny Moldovanu & Philipp Strack, 2021. "Extreme Points and Majorization: Economic Applications," Econometrica, Econometric Society, vol. 89(4), pages 1557-1593, July.
    3. Rick Harbaugh & Eric Rasmusen, 2018. "Coarse Grades: Informing the Public by Withholding Information," American Economic Journal: Microeconomics, American Economic Association, vol. 10(1), pages 210-235, February.
    4. Matthew Gentzkow & Emir Kamenica, 2016. "A Rothschild-Stiglitz Approach to Bayesian Persuasion," American Economic Review, American Economic Association, vol. 106(5), pages 597-601, May.
    5. Goldstein, Itay & Leitner, Yaron, 2018. "Stress tests and information disclosure," Journal of Economic Theory, Elsevier, vol. 177(C), pages 34-69.
    6. Anton Kolotilin & Alexander Wolitzky, 2020. "Assortative Information Disclosure," Discussion Papers 2020-08, School of Economics, The University of New South Wales.
    7. Yingni Guo & Eran Shmaya, 2019. "The Interval Structure of Optimal Disclosure," Econometrica, Econometric Society, vol. 87(2), pages 653-675, March.
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    Citations

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    Cited by:

    1. Roberto Corrao & Yifan Dai, 2023. "The Bounds of Mediated Communication," Papers 2303.06244, arXiv.org, revised Nov 2023.
    2. Zeng, Yishu, 2023. "Derandomization of persuasion mechanisms," Journal of Economic Theory, Elsevier, vol. 212(C).
    3. Kai Hao Yang & Alexander K. Zentefis, 2023. "Monotone Function Intervals: Theory and Applications," Papers 2302.03135, arXiv.org, revised Apr 2024.
    4. Qianjun Lyu & Wing Suen & Yimeng Zhang, 2023. "Coarse Information Design," Papers 2305.18020, arXiv.org, revised May 2024.
    5. Federico Echenique & Teddy Mekonnen & M. Bumin Yenmez, 2024. "Diversity in Choice as Majorization," Papers 2407.17589, arXiv.org.
    6. Atulya Jain & Vianney Perchet, 2024. "Calibrated Forecasting and Persuasion," Papers 2406.15680, arXiv.org.
    7. Lily Ling Yang, 2024. "Information Design with Costly State Verifi cation," CRC TR 224 Discussion Paper Series crctr224_2024_502, University of Bonn and University of Mannheim, Germany.

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    More about this item

    Keywords

    Bayesian persuasion; mean preserving contraction; bi-pooling; information disclosure; price function; signaling; extreme points;
    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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