Continuous-time persuasion by filtering

TL;DR

This paper develops a continuous-time dynamic persuasion model using stochastic control with partial observations, providing theoretical results and applications in energy and environmental management.

Contribution

It introduces a linear-quadratic framework for dynamic persuasion with commitment, proves a verification theorem for the HJB equation, and extends to mean field interactions.

Findings

Information provision affects electricity pricing.

Carbon footprint rules influence corporate emissions strategies.

The model offers a new approach to strategic information design.

Abstract

We frame dynamic persuasion in a partial observation stochastic control Leader-Follower game with an ergodic criterion. The Receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the Receiver through a device designed by the Sender that generates the observation process. The commitment of the Sender is enforced. We develop this approach in the case where all dynamics are linear and the preferences of the Receiver are linear-quadratic. We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the Receiver's value function. An extension to the case of persuasion of a mean field of interacting Receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that information provision is a substitute for best-in-class objective.