Persuasion with limited communication capacity

TL;DR

This paper analyzes a Bayesian persuasion scenario with limited, noisy communication channels, establishing an upper bound on the persuader's payoff and showing how to approach this bound using strategies linked to the channel's information capacity.

Contribution

It provides a tight upper bound on persuasion payoffs under communication constraints and characterizes the optimal strategies in large independent problem settings.

Findings

Upper bound on persuader's payoff with limited communication

Strategies can approach the bound as the number of problems grows

Optimal payoff relates to the channel's information capacity

Abstract

We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on the payoffs the persuader can secure by communicating through the channel. We also show that the bound is tight, i.e., if the persuasion problem consists of a large number of independent copies of the same base problem, then the persuader can achieve this bound arbitrarily closely by using strategies that tie all the problems together. We characterize this optimal payoff as a function of the information-theoretic capacity of the communication channel.