DP15859 Optimal Transport of Information
|Author(s):||Anna Cieslak, Semyon Malamud, Andreas Schrimpf|
|Publication Date:||February 2021|
|Date Revised:||March 2021|
|Keyword(s):||Bayesian persuasion, information design, signalling|
|Programme Areas:||Financial Economics|
|Link to this Page:||cepr.org/active/publications/discussion_papers/dp.php?dpno=15859|
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.