Algorithms for Persuasion with Limited Communication

TL;DR

This paper investigates the computational complexity of designing optimal signaling schemes in Bayesian persuasion, demonstrating tractability under certain distributional assumptions and providing algorithms for symmetric and independent cases.

Contribution

It introduces polynomial-time algorithms for symmetric distributions and a constant-factor approximation for independent distributions, overcoming general NP-hardness.

Findings

Optimal signaling schemes are tractable under symmetry assumptions.

A polynomial-time algorithm for symmetric distributions is developed.

A constant-factor approximation algorithm is proposed for independent distributions.

Abstract

The Bayesian persuasion paradigm of strategic communication models interaction between a privately-informed agent, called the sender, and an ignorant but rational agent, called the receiver. The goal is typically to design a (near-)optimal communication (or signaling) scheme for the sender. It enables the sender to disclose information to the receiver in a way as to incentivize her to take an action that is preferred by the sender. Finding the optimal signaling scheme is known to be computationally difficult in general. This hardness is further exacerbated when there is also a constraint on the size of the message space, leading to NP-hardness of approximating the optimal sender utility within any constant factor. In this paper, we show that in several natural and prominent cases the optimization problem is tractable even when the message space is limited. In particular, we study signaling under a symmetry or an independence assumption on the distribution of utility values for the actions. For symmetric distributions, we provide a novel characterization of the optimal signaling scheme. It results in a polynomial-time algorithm to compute an optimal scheme for many compactly represented symmetric distributions. In the independent case, we design a constant-factor approximation algorithm, which stands in marked contrast to the hardness of approximation in the general case.