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Persuasion and Matching: Optimal Productive Transport

Author

Listed:
  • Anton Kolotilin

    (School of Economics, UNSW)

  • Roberto Corrao

    (Department of Economics, MIT)

  • Alexander Wolitzky

    (Department of Economics, MIT)

Abstract

We consider general Bayesian persuasion problems where the receiver’s utility is single-peaked in a one-dimensional action. We show that a signal that pools at most two states in each realization is always optimal, and that such pairwise signals are the only solutions under a non-singularity condition (the twist condition). Our core results provide conditions under which riskier prospects induce higher or lower actions, so that the induced action is single-dipped or single-peaked on each set of nested prospects. We also provide conditions for the optimality of either full disclosure or negative assortative disclosure, where all prospects are nested. Methodologically, our results rely on novel duality and complementary slackness theorems. Our analysis extends to a general problem of assigning one-dimensional inputs to productive units, which we call optimal productive transport. This problem covers additional applications including club economies (assigning workers to firms, or students to schools), robust option pricing (assigning future asset prices to price distributions), and partisan gerrymandering (assigning voters to districts).

Suggested Citation

  • Anton Kolotilin & Roberto Corrao & Alexander Wolitzky, 2023. "Persuasion and Matching: Optimal Productive Transport," Discussion Papers 2023-12, School of Economics, The University of New South Wales.
    • Handle: RePEc:swe:wpaper:2023-12
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    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2023-12.pdf
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    References listed on IDEAS

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    6. Matthew Gentzkow & Emir Kamenica, 2016. "A Rothschild-Stiglitz Approach to Bayesian Persuasion," American Economic Review, American Economic Association, vol. 106(5), pages 597-601, May.
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    10. Alex Smolin & Takuro Yamashita, 2022. "Information Design in Smooth Games," Papers 2202.10883, arXiv.org, revised Dec 2023.
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    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Hedlund, Jonas, 2024. "Signaling through Bayesian persuasion," Mathematical Social Sciences, Elsevier, vol. 132(C), pages 15-27.
    2. Daniel Quigley & Ansgar Walther, 2024. "Inside and Outside Information," Journal of Finance, American Finance Association, vol. 79(4), pages 2667-2714, August.
    3. Emir Kamenica & Xiao Lin, 2024. "Commitment and Randomization in Communication," Papers 2410.17503, arXiv.org.
    4. Emir Kamenica & Xiao Lin, 2024. "Commitment and Randomization in Communication," PIER Working Paper Archive 24-033, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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    More about this item

    Keywords

    Bayesian persuasion; information design; first-order approach; optimal transport; duality; complementary slackness; pairwise signal; single-dipped signal; negative assortative disclosure; club economies; option pricing; gerrymandering;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • 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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