Algorithmic Persuasion with No Externalities

Abstract

We study the algorithmics of information structure design -a.k.a. persuasion or signaling -in a fundamental special case introduced by Arieli and Babichenko: multiple agents, binary actions, and no inter-agent externalities. Unlike prior work on this model, we allow many states of nature. We assume that the principal's objective is a monotone set function, and study the problem both in the public signal and private signal models, drawing a sharp contrast between the two in terms of both efficacy and computational complexity.When private signals are allowed, our results are largely positive and quite general. First, we use linear programming duality and the equivalence of separation and optimization to show polynomial-time equivalence between (exactly) optimal signaling and the problem of maximizing the objective function plus an additive function. This yields an efficient implementation of the optimal scheme when the objective is supermodular or anonymous. Second, we exhibit a (1 − 1/e)-approximation of the optimal private signaling scheme, modulo an additive loss of ǫ, when the objective function is submodular. These two results simplify, unify, and generalize results of [3,4], extending them from a binary state of nature to many states (modulo the additive loss in the latter result). Third, we consider the binary-state case with a submodular objective, and simplify and slightly strengthen the result of [4] to obtain a (1 − 1/e)-approximation via a scheme which (i) signals independently to each receiver and (ii) is "oblivious" in that it does not depend on the objective function so long as it is monotone submodular.When only a public signal is allowed, our results are negative. First, we show that it is NP-hard to approximate the optimal public scheme, within any constant factor, even when the objective is additive. Second, we show that the optimal private scheme can outperform the optimal public scheme, in terms of maximizing the sender's objective, by a polynomial factor.

Optimal Algorithm for Bayesian Incentive-Compatible Exploration

“…Consequently, the right-hand sides are also non-negative. So from (5) we deduce −1 < µ j < i j j+1 and from (6) and the induction hypothesis we deduce ω j t +1 ≥ i j t and as a result, i j t +1 ≥ i j t . L 5.8.…”

“…Another related topic is that of Bayesian Persuasion by Kamenica and Gentzkow [9] where the planner tries to infer a value of an "unobservable" state using interaction with multiple agents. See [4][5][6] for a more algorithmic perspective of Bayesian Persuasion.…”

Persuasion and Incentives Through the Lens of Duality

“…Bayesian persuasion with multiple agents, binary actions and externalities. In this paper, we formalize a model with externalities, naturally extending the model introduced recently in Arieli and Babichenko [2019] and Dughmi and Xu [2017] for private persuasion with no externalities. Consider the general setup of Bayesian persuasion with one sender and N receivers, where each receiver can take either action 0 or action 1.…”

“…In this section, we study Bayesian persuasion for multiple receivers with binary actions and general externalities through the lens of duality. Our model is a natural extension of the model recently introduced in Arieli and Babichenko [2019], and further developed in Dughmi and Xu [2017]. We refer the reader to Section 2 for notation and definitions.…”

“…We work with two models of persuasion: the Bayesian Persuasion model of Kamenica and Gentzkow [2011], and the multi-receiver private Bayesian persuasion model of Arieli and Babichenko [2019] (further developed in Babichenko and Barman [2017] and Dughmi and Xu [2017]) which we generalize to allow externalities. In the spirit of mechanism design and principal-agent problems, we generalize both models by permitting payments, which serve as additional incentive for the receiver(s) of information to behave in accordance with the wishes of the sender (principal).…”