Persuasion by Dimension Reduction

107 Pages Posted: 22 Oct 2021 Last revised: 26 Oct 2021

See all articles by Semyon Malamud

Semyon Malamud

Ecole Polytechnique Federale de Lausanne; Centre for Economic Policy Research (CEPR); Swiss Finance Institute

Andreas Schrimpf

Bank for International Settlements (BIS) - Monetary and Economic Department; Centre for Economic Policy Research (CEPR); University of Tuebingen

Date Written: October 17, 2021

Abstract

How should an agent (the sender) observing multi-dimensional data (the state vector) persuade another agent to take the desired action? We show that it is always optimal for the sender to perform a (non-linear) dimension reduction by projecting the state vector onto a lower-dimensional object that we call the "optimal information manifold." We characterize geometric properties of this manifold and link them to the sender's preferences. Optimal policy splits information into "good" and "bad" components. When the sender's marginal utility is linear, it is always optimal to reveal the full magnitude of good information. In contrast, with concave marginal utility, optimal information design conceals the extreme realizations of good information and only reveals its direction (sign). We illustrate these effects by explicitly solving several multi-dimensional Bayesian persuasion problems.

Keywords: Bayesian Persuasion, Information Design, Signalling, Learning

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

Suggested Citation

Malamud, Semyon and Schrimpf, Andreas, Persuasion by Dimension Reduction (October 17, 2021). Swiss Finance Institute Research Paper No. 21-69, Available at SSRN: https://ssrn.com/abstract=3946389 or http://dx.doi.org/10.2139/ssrn.3946389

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

Andreas Schrimpf

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

Centralbahnplatz 2
CH-4002 Basel
Switzerland

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

University of Tuebingen ( email )

Wilhelmstr. 19
72074 Tuebingen, Baden Wuerttemberg 72074
Germany

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