Report
Optimal Transport of Information
| العنوان: | Optimal Transport of Information |
|---|---|
| المؤلفون: | Malamud, Semyon, Cieslak, Anna, Schrimpf, Andreas |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics Quantitative Finance Statistics |
| مصطلحات موضوعية: | Economics - General Economics, Mathematics - Optimization and Control, Statistics - Other Statistics |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2102.10909 |
| رقم الانضمام: | edsarx.2102.10909 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |