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Title: Optimal Transport of Information

Author(s): Anna Cieslak, Semyon Malamud and Andreas Schrimpf

Publication Date: February 2021

Keyword(s): Bayesian persuasion, information design and signalling

Programme Area(s): Financial Economics

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.

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Bibliographic Reference

Cieslak, A, Malamud, S and Schrimpf, A. 2021. 'Optimal Transport of Information'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=15859