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Optimal Transport of Information

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  • Malamud, Semyon
  • Cieslak, Anna
  • Schrimpf, Paul

Abstract

We study the general problem of Bayesian persuasion (optimal information design) with continuous actions and continuous state space in arbitrary dimensions. First, we show that with a finite signal space, the optimal information design is always given by a partition. Second, we take the limit of an infinite signal space and characterize the solution in terms of a Monge-Kantorovich optimal transport problem with an endogenous information transport cost. We use our novel approach to: 1. Derive necessary and sufficient conditions for optimality based on Bregman divergences for non-convex functions. 2. Compute exact bounds for the Hausdorff dimension of the support of an optimal policy. 3. Derive a non-linear, second-order partial differential equation whose solutions correspond to regular optimal policies. We illustrate the power of our approach by providing explicit solutions to several non-linear, multidimensional Bayesian persuasion problems.

Suggested Citation

  • Malamud, Semyon & Cieslak, Anna & Schrimpf, Paul, 2021. "Optimal Transport of Information," CEPR Discussion Papers 15859, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:15859
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    References listed on IDEAS

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    Cited by:

    1. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2023. "Persuasion as Transportation," Papers 2307.07672, arXiv.org.

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    More about this item

    Keywords

    Bayesian persuasion; Information design; Signalling;
    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

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