Public Bayesian Persuasion: Being Almost Optimal and Almost Persuasive

• URL: http://arxiv.org/abs/2002.05156v2
• Date: Tue, 31 Mar 2020 13:26:27 GMT
• Title: Public Bayesian Persuasion: Being Almost Optimal and Almost Persuasive
• Authors: Matteo Castiglioni, Andrea Celli, Nicola Gatti
• Abstract summary: 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 provide a quasi-polynomial time bi-criteria approximation algorithm for arbitrary public persuasion problems that, in specific settings, yields a QPTAS.
• Score: 57.47546090379434
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Persuasion studies how an informed principal may influence the behavior of agents by the strategic provision of payoff-relevant information. We focus on the fundamental multi-receiver model by Arieli and Babichenko (2019), in which there are no inter-agent 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 bi-criteria 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 quasi-polynomial 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 quasi-polynomial time to be solved. Finally, we close the gap by providing a quasi-polynomial time bi-criteria approximation algorithm for arbitrary public persuasion problems that, in specific settings, yields a QPTAS.

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