TY - GEN
T1 - Algorithms for persuasion with limited communication
AU - Gradwohl, Ronen
AU - Hahn, Niklas
AU - Hoefer, Martin
AU - Smorodinsky, Rann
N1 - Publisher Copyright:
Copyright © 2021 by SIAM
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85105295119&partnerID=8YFLogxK
M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???
AN - SCOPUS:85105295119
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 637
EP - 652
BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
A2 - Marx, Daniel
T2 - 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2021
Y2 - 10 January 2021 through 13 January 2021
ER -