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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 which has a fixed and limited number of messages and is subject to exogenous noise. Imperfect communication entails a loss of payoff for the persuader. We establish an upper bound on the payoffs the persuader can secure by communicating through the channel. We also show that the bound is tight: 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 which 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, 2017. "Persuasion with Limited Communication Capacity," HEC Research Papers Series 1244, HEC Paris.
    • Handle: RePEc:ebg:heccah:1244
    DOI: 10.2139/ssrn.3083932
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    Cited by:

    1. Yaron Azrieli & Rachana Das, 2025. "Sequential Non-Bayesian Persuasion," Papers 2508.09464, arXiv.org.
    2. Koessler, Frederic & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Long information design," Theoretical Economics, Econometric Society, vol. 17(2), May.
    3. 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.
    4. Hyeonggyun Ko, 2025. "Persuasion in the Long Run: When history matters," Papers 2508.01662, arXiv.org.
    5. 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.
    6. Sosung Baik & Sung-Ha Hwang, 2021. "Auction design with ambiguity: Optimality of the first-price and all-pay auctions," Papers 2110.08563, arXiv.org.
    7. Koessler, Frederic & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Long information design," Theoretical Economics, Econometric Society, vol. 17(2), May.
    8. Matysková, Ludmila & Montes, Alfonso, 2023. "Bayesian persuasion with costly information acquisition," Journal of Economic Theory, Elsevier, vol. 211(C).
    9. Lian, Zeng & Xu, Shuo & Zheng, Jie, 2025. "Entrant-optimal learning in a contest game," Journal of Mathematical Economics, Elsevier, vol. 120(C).
    10. Eilat, Ran & Neeman, Zvika, 2023. "Communication with endogenous deception costs," Journal of Economic Theory, Elsevier, vol. 207(C).
    11. 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.
    12. Laura Doval & Vasiliki Skreta, 2022. "Mechanism Design With Limited Commitment," Econometrica, Econometric Society, vol. 90(4), pages 1463-1500, July.
    13. Hedlund, Jonas, 2024. "Signaling through Bayesian persuasion," Mathematical Social Sciences, Elsevier, vol. 132(C), pages 15-27.
    14. Ian M. Schmutte & Nathan Yoder, 2022. "Information Design for Differential Privacy," Papers 2202.05452, arXiv.org, revised Jul 2024.
    15. Laura Doval & Vasiliki Skreta, 2018. "Constrained Information Design," Papers 1811.03588, arXiv.org, revised Aug 2022.
    16. Reema Deori & Ankur A. Kulkarni, 2024. "Informativeness and Trust in Bayesian Persuasion," Papers 2408.13822, arXiv.org.
    17. Shih-Tang Su & Vijay G. Subramanian & Grant Schoenebeck, 2021. "Bayesian Persuasion in Sequential Trials," Papers 2110.09594, arXiv.org, revised Nov 2021.
    18. Eitan Sapiro-Gheiler, 2022. "Discovery through Trial Balloons," Papers 2211.02743, arXiv.org, revised Nov 2022.
    19. Tsakas, Elias & Tsakas, Nikolas, 2021. "Noisy persuasion," Games and Economic Behavior, Elsevier, vol. 130(C), pages 44-61.
    20. Yunus C. Aybas & Eray Turkel, 2019. "Persuasion with Coarse Communication," Papers 1910.13547, arXiv.org, revised May 2024.
    21. Mark Whitmeyer, 2019. "Bayesian Elicitation," Papers 1902.00976, arXiv.org, revised Feb 2024.
    22. Dworczak, Piotr & Kolotilin, Anton, 2024. "The persuasion duality," Theoretical Economics, Econometric Society, vol. 19(4), November.
    23. Yaron Azrieli, 2021. "Constrained versus Unconstrained Rational Inattention," Games, MDPI, vol. 12(1), pages 1-22, January.

    More about this item

    Keywords

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    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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