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Persuasion with limited communication capacity

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  • Le Treust, Maël
  • Tomala, Tristan

Abstract

We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on the payoffs the persuader can secure by communicating through the channel. We also show that the bound is tight, i.e., if the persuasion problem consists of a large number of independent copies of the same base problem, then the persuader can achieve this bound arbitrarily closely by using strategies that tie all the problems together. We characterize this optimal payoff as a function of the information-theoretic capacity of the communication channel.

Suggested Citation

  • Le Treust, Maël & Tomala, Tristan, 2019. "Persuasion with limited communication capacity," Journal of Economic Theory, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jetheo:v:184:y:2019:i:c:s0022053118305064
    DOI: 10.1016/j.jet.2019.104940
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    Citations

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    Cited by:

    1. Koessler, Frederic & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Long information design," Theoretical Economics, Econometric Society, vol. 17(2), May.
    2. 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.
    3. Vora, Anuj S. & Kulkarni, Ankur A., 2024. "Shannon meets Myerson: Information extraction from a strategic sender," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 48-66.
    4. Sosung Baik & Sung-Ha Hwang, 2021. "Auction design with ambiguity: Optimality of the first-price and all-pay auctions," Papers 2110.08563, arXiv.org.
    5. Koessler, Frederic & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Long information design," Theoretical Economics, Econometric Society, vol. 17(2), May.
    6. Matysková, Ludmila & Montes, Alfonso, 2023. "Bayesian persuasion with costly information acquisition," Journal of Economic Theory, Elsevier, vol. 211(C).
    7. Eilat, Ran & Neeman, Zvika, 2023. "Communication with endogenous deception costs," Journal of Economic Theory, Elsevier, vol. 207(C).
    8. Monte, Daniel & Linhares, Luis Henrique, 2023. "Stealth Startups, Clauses, and Add-ons: A Model of Strategic Obfuscation," MPRA Paper 115926, University Library of Munich, Germany.
    9. Laura Doval & Vasiliki Skreta, 2022. "Mechanism Design With Limited Commitment," Econometrica, Econometric Society, vol. 90(4), pages 1463-1500, July.
    10. Ian M. Schmutte & Nathan Yoder, 2022. "Information Design for Differential Privacy," Papers 2202.05452, arXiv.org, revised Jul 2024.
    11. Laura Doval & Vasiliki Skreta, 2018. "Constrained Information Design," Papers 1811.03588, arXiv.org, revised Aug 2022.
    12. Reema Deori & Ankur A. Kulkarni, 2024. "Informativeness and Trust in Bayesian Persuasion," Papers 2408.13822, arXiv.org.
    13. Shih-Tang Su & Vijay G. Subramanian & Grant Schoenebeck, 2021. "Bayesian Persuasion in Sequential Trials," Papers 2110.09594, arXiv.org, revised Nov 2021.
    14. Tsakas, Elias & Tsakas, Nikolas, 2021. "Noisy persuasion," Games and Economic Behavior, Elsevier, vol. 130(C), pages 44-61.
    15. Eitan Sapiro-Gheiler, 2022. "Discovery through Trial Balloons," Papers 2211.02743, arXiv.org, revised Nov 2022.
    16. Yunus C. Aybas & Eray Turkel, 2019. "Persuasion with Coarse Communication," Papers 1910.13547, arXiv.org, revised May 2024.
    17. Mark Whitmeyer, 2019. "Bayesian Elicitation," Papers 1902.00976, arXiv.org, revised Feb 2024.
    18. Yaron Azrieli, 2021. "Constrained versus Unconstrained Rational Inattention," Games, MDPI, vol. 12(1), pages 1-22, January.

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    More about this item

    Keywords

    Bayesian persuasion; Communication channel; Mutual information;
    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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