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Persuasion by Dimension Reduction

Author

Listed:
  • Semyon Malamud

    (Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute)

  • Andreas Schrimpf

    (Bank for International Settlements (BIS) - Monetary and Economic Department; CREATES - Aarhus University)

Abstract

How should an agent (the sender) observing multi-dimensional data (the state vector) persuade another agent to take the desired action? We show that it is always optimal for the sender to perform a (non-linear) dimension reduction by projecting the state vector onto a lower-dimensional object that we call the "optimal information manifold." We characterize geometric properties of this manifold and link them to the sender's preferences. Optimal policy splits information into "good" and "bad" components. When the sender's marginal utility is linear, it is always optimal to reveal the full magnitude of good information. In contrast, with concave marginal utility, optimal information design conceals the extreme realizations of good information and only reveals its direction (sign). We illustrate these effects by explicitly solving several multi-dimensional Bayesian persuasion problems.

Suggested Citation

  • Semyon Malamud & Andreas Schrimpf, 2021. "Persuasion by Dimension Reduction," Swiss Finance Institute Research Paper Series 21-69, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp2169
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    Cited by:

    1. Alex Smolin & Takuro Yamashita, 2022. "Information Design in Smooth Games," Papers 2202.10883, arXiv.org, revised Jul 2025.
    2. Van Der Straeten, Karine & Yamashita, Takuro, 2023. "On the veil-of-ignorance principle: welfare-optimal information disclosure in Voting," TSE Working Papers 23-1463, Toulouse School of Economics (TSE), revised Mar 2025.
    3. Takuro Yamashita & Alex Smolin, 2022. "Information design in concave games," Post-Print hal-04141179, HAL.

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    Keywords

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    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
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E58 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Central Banks and Their Policies
    • E61 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Policy Objectives; Policy Designs and Consistency; Policy Coordination

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