Entropy-Regularized Optimal Transport in Information Design

TL;DR

This paper introduces an entropy-regularized optimal transport approach to optimize information policies in strategic communication, revealing structural properties and extending to multi-product scenarios.

Contribution

It develops an efficient algorithm for entropy-regularized optimal transport in information design and explores its application to multi-product monopolist problems.

Findings

Optimal configurations exhibit specific qualitative properties.

The method efficiently computes solutions for complex information policies.

Extensions to multi-product scenarios demonstrate versatility.

Abstract

In this paper, we explore a scenario where a sender provides an information policy and a receiver, upon observing a realization of this policy, decides whether to take a particular action, such as making a purchase. The sender's objective is to maximize her utility derived from the receiver's action, and she achieves this by careful selection of the information policy. Building on the work of Kleiner et al., our focus lies specifically on information policies that are associated with power diagram partitions of the underlying domain. To address this problem, we employ entropy-regularized optimal transport, which enables us to develop an efficient algorithm for finding the optimal solution. We present experimental numerical results that highlight the qualitative properties of the optimal configurations, providing valuable insights into their structure. Furthermore, we extend our numerical investigation to derive optimal information policies for monopolists dealing with multiple products, where the sender discloses information about product qualities.