Persuasion with Coarse Communication

TL;DR

This paper investigates how limited message capacity affects an expert's ability to persuade, revealing that more signals don't always lead to better communication and that coarser messages can sometimes be preferable.

Contribution

It introduces a geometric framework for analyzing persuasion with limited communication and characterizes the impact of additional signals on persuasion effectiveness.

Findings

Additional signals can increase persuasion value in certain games.

More signals do not necessarily mean more information transmitted.

Coarser communication can be optimal and beneficial for welfare.

Abstract

In many real-world scenarios, experts must convey complex information with limited message capacity. This paper explores how the availability of messages influences an expert's persuasive ability. We develop a geometric representation of the expert's payoff with limited message capacity and identify bounds on the value of an additional signal for the sender. In a special class of games, the marginal value of a signal increases as the receiver becomes more difficult to persuade. Moreover, we show that access to an additional signal does not necessarily translate into more information transmitted in equilibrium, and the receiver might prefer coarser communication. This suggests that regulations on communication capacity have the potential to shift the balance of power from the expert to the decision-maker, ultimately improving welfare. Finally, we study the geometric properties of optimal information structures and show that the complexity of the sender's problem can be simplified to a finite algorithm.