Optimal Transport of Information

72 Pages Posted: 23 Feb 2021 Last revised: 8 Mar 2021

See all articles by Semyon Malamud

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)

Andreas Schrimpf

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

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Date Written: February 22, 2021

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.

Keywords: Bayesian Persuasion, Information Design, Signalling, Optimal Transport

JEL Classification: D82, D83, E52, E58, E61

Suggested Citation

Malamud, Semyon and Cieslak, Anna and Schrimpf, Andreas and Schrimpf, Andreas, Optimal Transport of Information (February 22, 2021). Swiss Finance Institute Research Paper No. 21-15, Available at SSRN: https://ssrn.com/abstract=3790542 or http://dx.doi.org/10.2139/ssrn.3790542

Semyon Malamud (Contact Author)

Ecole Polytechnique Federale de Lausanne ( email )

Lausanne, 1015
Switzerland

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Anna Cieslak

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States
919 660 7879 (Phone)

HOME PAGE: https://sites.google.com/site/ancieslak/

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Andreas Schrimpf

CREATES - Aarhus University ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Bank for International Settlements (BIS) - Monetary and Economic Department ( email )

Centralbahnplatz 2
CH-4002 Basel
Switzerland

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