Bayesian Persuasion with Externalities: Exploiting Agent Types

TL;DR

This paper explores how a principal can optimally signal information to multiple agents with externalities, considering agent types and different signaling channels, providing computational methods and complexity results.

Contribution

It introduces a framework for Bayesian persuasion with externalities, characterizes optimal strategies, and analyzes computational complexity across various signaling models.

Findings

Optimal signaling strategies characterized via linear programs

Polynomial-time algorithms for bounded deviation cases

NP-hardness results for unbounded deviation scenarios

Abstract

We study a Bayesian persuasion problem with externalities. In this model, a principal sends signals to inform multiple agents about the state of the world. Simultaneously, due to the existence of externalities in the agents' utilities, the principal also acts as a correlation device to correlate the agents' actions. We consider the setting where the agents are categorized into a small number of types. Agents of the same type share identical utility functions and are treated equitably in the utility functions of both other agents and the principal. We study the problem of computing optimal signaling strategies for the principal, under three different types of signaling channels: public, private, and semi-private. Our results include revelation-principle-style characterizations of optimal signaling strategies, linear programming formulations, and analysis of in/tractability of the optimization problems. It is demonstrated that when the maximum number of deviating agents is bounded by a constant, our LP-based formulations compute optimal signaling strategies in polynomial time. Otherwise, the problems are NP-hard.