Algorithmic Bayesian persuasion with combinatorial actions

TL;DR

This paper investigates the computational complexity of designing signaling schemes in Bayesian persuasion with combinatorial action constraints, providing hardness results and efficient algorithms under certain conditions.

Contribution

It introduces polynomial-time algorithms for Bayesian persuasion with matroid constraints assuming a fixed number of states, and explores relaxed persuasiveness notions.

Findings

Constant-factor approximation NP-hardness in some cases

Polynomial-time algorithm for matroids with fixed states

Sufficient conditions for polynomial-time approximability under CCE-persuasiveness

Abstract

Bayesian persuasion is a model for understanding strategic information revelation: an agent with an informational advantage, called a sender, strategically discloses information by sending signals to another agent, called a receiver. In algorithmic Bayesian persuasion, we are interested in efficiently designing the sender's signaling schemes that lead the receiver to take action in favor of the sender. This paper studies algorithmic Bayesian-persuasion settings where the receiver's feasible actions are specified by combinatorial constraints, e.g., matroids or paths in graphs. We first show that constant-factor approximation is NP-hard even in some special cases of matroids or paths. We then propose a polynomial-time algorithm for general matroids by assuming the number of states of nature to be a constant. We finally consider a relaxed notion of persuasiveness, called CCE-persuasiveness, and present a sufficient condition for polynomial-time approximability.