Working Paper: CEPR ID: DP15859
Authors: Semyon Malamud; Anna Cieslak; Andreas Schrimpf
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 Codes: D82; D83; E52; E58; E61
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| optimal information design (partition) (D80) | actions of receivers (G34) |
| Monge-Kantorovich optimal transport problem (C61) | design of information (L86) |
| choice of information design (Y10) | utility derived from receiver actions (D46) |
| dimensionality of the information space (D83) | effectiveness of the design (C90) |
| nonlinear second-order partial differential equations (C69) | regular optimal policies (C54) |