IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2507.03203.html
   My bibliography  Save this paper

Data-Driven Persuasion

Author

Listed:
  • Maxwell Rosenthal

Abstract

This paper develops a data-driven approach to Bayesian persuasion. The receiver is privately informed about the prior distribution of the state of the world, the sender knows the receiver's preferences but does not know the distribution of the state variable, and the sender's payoffs depend on the receiver's action but not on the state. Prior to interacting with the receiver, the sender observes the distribution of actions taken by a population of decision makers who share the receiver's preferences in best response to an unobserved distribution of messages generated by an unknown and potentially heterogeneous signal. The sender views any prior that rationalizes this data as plausible and seeks a signal that maximizes her worst-case payoff against the set of all such distributions. We show positively that the two-state many-action problem has a saddle point and negatively that the two-action many-state problem does not. In the former case, we identify adversarial priors and optimal signals. In the latter, we characterize the set of robustly optimal Blackwell experiments.

Suggested Citation

  • Maxwell Rosenthal, 2025. "Data-Driven Persuasion," Papers 2507.03203, arXiv.org, revised Aug 2025.
    • Handle: RePEc:arx:papers:2507.03203
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2507.03203
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lorenzo Magnolfi & Camilla Roncoroni, 2023. "Estimation of Discrete Games with Weak Assumptions on Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(4), pages 2006-2041.
    2. Kosterina, Svetlana, 2022. "Persuasion with unknown beliefs," Theoretical Economics, Econometric Society, vol. 17(3), July.
    3. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2022. "Counterfactuals with Latent Information," American Economic Review, American Economic Association, vol. 112(1), pages 343-368, January.
    4. Babichenko, Yakov & Talgam-Cohen, Inbal & Xu, Haifeng & Zabarnyi, Konstantin, 2022. "Regret-minimizing Bayesian persuasion," Games and Economic Behavior, Elsevier, vol. 136(C), pages 226-248.
    5. Piotr Dworczak & Alessandro Pavan, 2022. "Preparing for the Worst but Hoping for the Best: Robust (Bayesian) Persuasion," Econometrica, Econometric Society, vol. 90(5), pages 2017-2051, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tommaso Denti & Doron Ravid, 2023. "Robust Predictions in Games with Rational Inattention," Papers 2306.09964, arXiv.org.
    2. Maxim Senkov & Toygar T. Kerman, 2024. "Changing Simplistic Worldviews," Papers 2401.02867, arXiv.org.
    3. Eitan Sapiro-Gheiler, 2024. "Persuasion with ambiguous receiver preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(4), pages 1173-1218, June.
    4. Henrique de Oliveira & Rohit Lamba, 2025. "Rationalizing dynamic choices," Papers 2504.05251, arXiv.org.
    5. Kun Zhang, 2025. "Uncharted Waters: Selling a New Product Robustly," Papers 2508.04134, arXiv.org.
    6. Gualdani, Cristina & Sinha, Shruti, 2024. "Identification in discrete choice models with imperfect information," Journal of Econometrics, Elsevier, vol. 244(1).
    7. Alexei Parakhonyak & Anton Sobolev, 2022. "Persuasion without Priors," Economics Series Working Papers 977, University of Oxford, Department of Economics.
    8. Keegan Harris & Nicole Immorlica & Brendan Lucier & Aleksandrs Slivkins, 2023. "Algorithmic Persuasion Through Simulation," Papers 2311.18138, arXiv.org, revised Feb 2025.
    9. Krishnamurthy Iyer & Haifeng Xu & You Zu, 2023. "Markov Persuasion Processes with Endogenous Agent Beliefs," Papers 2307.03181, arXiv.org, revised Jul 2023.
    10. Alon, Shiri & Auster, Sarah & Gayer, Gabi & Minardi, Stefania, 2023. "Persuasion with Limited Data: A Case-Based Approach," CEPR Discussion Papers 18428, C.E.P.R. Discussion Papers.
    11. Babichenko, Yakov & Talgam-Cohen, Inbal & Xu, Haifeng & Zabarnyi, Konstantin, 2022. "Regret-minimizing Bayesian persuasion," Games and Economic Behavior, Elsevier, vol. 136(C), pages 226-248.
    12. Kocourek, Pavel & Steiner, Jakub & Stewart, Colin, 2024. "Boundedly rational demand," Theoretical Economics, Econometric Society, vol. 19(4), November.
    13. Yulia Evsyukova & Federico Innocenti & Niccolò Lomys, 2024. "Optimal Multiple Loan Contracting under Sequential Audits and Contagion Losses," CSEF Working Papers 743, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    14. Martin Richardson, 2021. "Of hired guns and ideologues: why would a law firm ever retain an honest expert witness?," ANU Working Papers in Economics and Econometrics 2021-678, Australian National University, College of Business and Economics, School of Economics.
    15. Ce Li & Tao Lin, 2024. "Information Design with Unknown Prior," Papers 2410.05533, arXiv.org, revised Sep 2025.
    16. Semyon Malamud & Andreas Schrimpf, 2021. "Persuasion by Dimension Reduction," Swiss Finance Institute Research Paper Series 21-69, Swiss Finance Institute.
    17. Xiaoyu Cheng, 2020. "Ambiguous Persuasion: An Ex-Ante Formulation," Papers 2010.05376, arXiv.org, revised Aug 2025.
    18. Inostroza, Nicolas A. & Pavan, Alessandro, 2025. "Adversarial coordination and public information design," Theoretical Economics, Econometric Society, vol. 20(2), May.
    19. Malamud, Semyon & Cieslak, Anna & Schrimpf, Paul, 2021. "Optimal Transport of Information," CEPR Discussion Papers 15859, C.E.P.R. Discussion Papers.
    20. Takashi Ui, 2022. "Optimal and Robust Disclosure of Public Information," Papers 2203.16809, arXiv.org, revised Apr 2022.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2507.03203. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.