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Private Bayesian persuasion

Author

Listed:
  • Arieli, Itai
  • Babichenko, Yakov

Abstract

We consider a multi-receiver Bayesian persuasion problem where an informed sender tries to persuade a group of receivers to adopt a certain product. The sender is allowed to commit to a signaling policy where she sends a private signal to every receiver. The utility of the sender is a function of the subset of adopters and the realized state. We first consider a setting with a binary state space and no payoff externalities among receivers. We characterize an optimal signaling policy and the maximal revenue to the sender for two different types of utility functions: supermodular, and anonymous submodular. In particular, for supermodular utilities we show that the optimal policy correlates positive recommendation to adopt the product as much as possible. We generalize these results to the case of a nonbinary state space. The result for supermodular utilities is generalized to the case where receivers have payoff externalities. We also provide a necessary and sufficient condition under which public and conditionally independent signaling policies are optimal.

Suggested Citation

  • Arieli, Itai & Babichenko, Yakov, 2019. "Private Bayesian persuasion," Journal of Economic Theory, Elsevier, vol. 182(C), pages 185-217.
    • Handle: RePEc:eee:jetheo:v:182:y:2019:i:c:p:185-217
    DOI: 10.1016/j.jet.2019.04.008
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    References listed on IDEAS

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    Cited by:

    1. Jerry Anunrojwong & Krishnamurthy Iyer & David Lingenbrink, 2024. "Persuading Risk-Conscious Agents: A Geometric Approach," Operations Research, INFORMS, vol. 72(1), pages 151-166, January.
    2. Gradwohl, Ronen & Heller, Yuval & Hillman, Arye, 2022. "Social Media and Democracy," MPRA Paper 113609, University Library of Munich, Germany.
    3. Frederic Koessler & Marco Scarsini & Tristan Tomala, 2021. "Correlated Equilibria in Large Anonymous Bayesian Games," Papers 2107.06312, arXiv.org, revised Sep 2023.
    4. Ehud Lehrer & Dimitry Shaiderman, 2022. "Markovian Persuasion with Stochastic Revelations," Papers 2204.08659, arXiv.org, revised May 2022.
    5. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2022. "Bayesian Persuasion with Mediators," Papers 2203.04285, arXiv.org, revised Sep 2022.
    6. Ronen Gradwohl & Yuval Heller & Arye Hillman, 2022. "Social Media and Democracy," Papers 2206.14430, arXiv.org.
    7. Ehud Lehrer & Dimitry Shaiderman, 2021. "Markovian Persuasion," Papers 2111.14365, arXiv.org.
    8. Frédéric Koessler & Vasiliki Skreta, 2023. "Informed Information Design," Journal of Political Economy, University of Chicago Press, vol. 131(11), pages 3186-3232.
    9. Skreta, Vasiliki & Koessler, Frédéric, 2021. "Information Design by an Informed Designer," CEPR Discussion Papers 15709, C.E.P.R. Discussion Papers.
    10. Victor Augias & Daniel M. A. Barreto, 2020. "Persuading a Wishful Thinker," Papers 2011.13846, arXiv.org, revised Nov 2023.
    11. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2023. "Persuasion as Transportation," Papers 2307.07672, arXiv.org.
    12. Solan, Eilon & Zhao, Chang, 2023. "When (not) to publicize inspection results," Journal of Economic Theory, Elsevier, vol. 210(C).
    13. Wei, Dong, 2021. "Persuasion under costly learning," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    14. Itai Arieli & Ivan Geffner & Moshe Tennenholtz, 2024. "Receiver-Oriented Cheap Talk Design," Papers 2401.03671, arXiv.org.
    15. Shraddha Pathak & Ankur A. Kulkarni, 2022. "A Scalable Bayesian Persuasion Framework for Epidemic Containment on Heterogeneous Networks," Papers 2207.11578, arXiv.org.
    16. Ronen Gradwohl & Niklas Hahn & Martin Hoefer & Rann Smorodinsky, 2020. "Reaping the Informational Surplus in Bayesian Persuasion," Papers 2006.02048, arXiv.org.
    17. Daehong Min, 2021. "Bayesian persuasion under partial commitment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 743-764, October.
    18. Kerman, Toygar & Herings, P. Jean-Jacques & Karos, Dominik, 2020. "Persuading Strategic Voters," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).
    19. Anastasia Antsygina & Mariya Teteryatnikova, 2023. "Optimal information disclosure in contests with stochastic prize valuations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 743-780, April.
    20. Dirk Bergemann & Paul Duetting & Renato Paes Leme & Song Zuo, 2021. "Calibrated Click-Through Auctions: An Information Design Approach," Cowles Foundation Discussion Papers 2285, Cowles Foundation for Research in Economics, Yale University.
    21. Hahn, Niklas & Hoefer, Martin & Smorodinsky, Rann, 2022. "The secretary recommendation problem," Games and Economic Behavior, Elsevier, vol. 134(C), pages 199-228.
    22. Hiroto Sato, 2023. "Robust implementation in sequential information design under supermodular payoffs and objective," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 269-285, June.
    23. Tetsuya Hoshino, 2022. "Multi‐Agent Persuasion: Leveraging Strategic Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(2), pages 755-776, May.

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    More about this item

    Keywords

    Bayesian persuasion; Supermodular utility; Submodular utility;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative 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
    • M37 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Advertising

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