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Bayesian persuasion by a privately informed sender

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  • Hedlund, Jonas

Abstract

This paper introduces private sender information in a game of Bayesian persuasion with monotonic sender preferences. I derive properties of increasing differences related to the precision of signals and use these to characterize the set of equilibria selected by the D1 criterion. These equilibria are either separating (i.e., the sender's choice of signal reveals his private information to the receiver) or fully disclosing (i.e., the outcome of the sender's chosen signal fully reveals the payoff-relevant state). Which of these two cases occurs is determined by the optimality properties of fully disclosing signals. If full disclosure is optimal for all sender types, then the equilibrium is fully disclosing. Otherwise, the equilibrium is fully separating, and incentive compatibility requires the sender to use signals that are strictly more informative than the ones that would be used under symmetric information. Therefore, when full disclosure is suboptimal, the sender incurs a cost in comparison to the symmetric information case, whereas the receiver benefits from better information.

Suggested Citation

  • Hedlund, Jonas, 2017. "Bayesian persuasion by a privately informed sender," Journal of Economic Theory, Elsevier, vol. 167(C), pages 229-268.
  • Handle: RePEc:eee:jetheo:v:167:y:2017:i:c:p:229-268
    DOI: 10.1016/j.jet.2016.11.003
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    2. Jesse Bull & Joel Watson, 2019. "Statistical evidence and the problem of robust litigation," RAND Journal of Economics, RAND Corporation, vol. 50(4), pages 974-1003, December.
    3. Cheng Li, 2020. "Centralized policymaking and informational lobbying," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 527-557, April.
    4. Alonso, Ricardo & Câmara, Odilon, 2018. "On the value of persuasion by experts," Journal of Economic Theory, Elsevier, vol. 174(C), pages 103-123.
    5. Kerman, Toygar & Herings, P. Jean-Jacques & Karos, Dominik, 2020. "Persuading Strategic Voters," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).
    6. Frédéric Koessler & Vasiliki Skreta, 2021. "Information Design by an Informed Designer," PSE Working Papers halshs-03107866, HAL.
    7. Elias Tsakas & Nikolas Tsakas & Dimitrios Xefteris, 2017. "Resisting Persuasion," University of Cyprus Working Papers in Economics 07-2017, University of Cyprus Department of Economics.
    8. Elias Tsakas & Nikolas Tsakas, 2018. "Noisy Persuasion," University of Cyprus Working Papers in Economics 11-2018, University of Cyprus Department of Economics.
    9. Frédéric Koessler & Vasiliki Skreta, 2021. "Information Design by an Informed Designer," Working Papers halshs-03107866, HAL.
    10. Bizzotto, Jacopo & Rüdiger, Jesper & Vigier, Adrien, 2020. "Testing, disclosure and approval," Journal of Economic Theory, Elsevier, vol. 187(C).
    11. Yanlin Chen & Jun Zhang, 2019. "Signaling by Bayesian Persuasion and Pricing Strategy. Short title: Disclosure and Price Signaling," Working Paper Series 2019/14, Economics Discipline Group, UTS Business School, University of Technology, Sydney.

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    More about this item

    Keywords

    Bayesian persuasion; Signaling; Information transmission;
    All these keywords.

    JEL classification:

    • 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
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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