Public Bayesian Persuasion: Being Almost Optimal and Almost Persuasive
Abstract
Persuasion studies how an informed principal may influence the behavior of agents by the strategic provision of payoffrelevant information. We focus on the fundamental multireceiver model by Arieli and Babichenko (2019), in which there are no interagent externalities. Unlike prior works on this problem, we study the public persuasion problem in the general setting with: (i) arbitrary state spaces; (ii) arbitrary action spaces; (iii) arbitrary sender's utility functions. We fully characterize the computational complexity of computing a bicriteria approximation of an optimal public signaling scheme. In particular, we show, in a voting setting of independent interest, that solving this problem requires at least a quasipolynomial number of steps even in settings with a binary action space, assuming the Exponential Time Hypothesis. In doing so, we prove that a relaxed version of the Maximum Feasible Subsystem of Linear Inequalities problem requires at least quasipolynomial time to be solved. Finally, we close the gap by providing a quasipolynomial time bicriteria approximation algorithm for arbitrary public persuasion problems that, in specific settings, yields a QPTAS.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.05156
 Bibcode:
 2020arXiv200205156C
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Artificial Intelligence;
 Computer Science  Computational Complexity