Optimal Transport of Information

Semyon Malamud, Anna Cieslak and Andreas Schrimpf
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Semyon Malamud: Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute
Anna Cieslak: Duke University - Fuqua School of Business; National Bureau of Economic Research (NBER)

No 21-15, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

Abstract: We study the general problem of 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.

Keywords: Bayesian Persuasion; Information Design; Signalling; Optimal Transport (search for similar items in EconPapers)
JEL-codes: D82 D83 E52 E58 E61 (search for similar items in EconPapers)
Pages: 66 pages
Date: 2021-02
New Economics Papers: this item is included in nep-mac and nep-mic
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Citations: View citations in EconPapers (1)

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https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3790542 (application/pdf)

Related works:
Working Paper: Optimal Transport of Information (2021)
Working Paper: Optimal Transport of Information (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp2115

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