Persuasion by Dimension Reduction
107 Pages Posted: 22 Oct 2021 Last revised: 26 Oct 2021
Date Written: October 17, 2021
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: Suggested Citation