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Optimal Transport of Information

Semyon Malamud, Anna Cieslak and Andreas Schrimpf

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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.

Date: 2021-02, Revised 2021-03
New Economics Papers: this item is included in nep-gth
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http://arxiv.org/pdf/2102.10909 Latest version (application/pdf)

Related works:
Working Paper: Optimal Transport of Information (2021) Downloads
Working Paper: Optimal Transport of Information (2021) Downloads
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