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Persuasion Without Priors

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  • Alexei Parakhonyak
  • Anton Sobolev

Abstract

We consider an information design problem when the sender faces ambiguity regarding the probability distribution over the states of the world, the utility function and the prior of the receiver. The solution concept is minimax loss (regret), that is, the sender minimizes the distance from the full information benchmark in the worst-case scenario. We show that in the binary states and binary actions setting the optimal strategy involves a mechanism with a continuum of messages, which admits a representation as a randomization over mechanisms consisting of two messages. A small level of uncertainty regarding the re- ceiver’s prior makes the sender more truthful than in the full information benchmark, but as uncertainty increases at some point the sender starts to lie more. If the sender either knows the probability distribution over the states of the world, or knows that the receiver knows it, then the maximal loss is bounded from above by 1/e. This result generalizes to an infinite state model, provided that the set of admissible mechanisms is limited to cut-off strategies.

Suggested Citation

  • Alexei Parakhonyak & Anton Sobolev, 2022. "Persuasion Without Priors," CRC TR 224 Discussion Paper Series crctr224_2022_359, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2022_359
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    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp359
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    References listed on IDEAS

    as
    1. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    2. Kosterina, Svetlana, 2022. "Persuasion with unknown beliefs," Theoretical Economics, Econometric Society, vol. 17(3), July.
    3. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    4. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415, World Scientific Publishing Co. Pte. Ltd..
    5. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, July.
    6. Emir Kamenica, 2019. "Bayesian Persuasion and Information Design," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 249-272, August.
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    More about this item

    Keywords

    Persuasion; Robustness; Multiple priors; Minimax regret;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • 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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