Algorithmic Bayesian persuasion

Dughmi, Shaddin; Xu, Haifeng

doi:10.1145/2897518.2897583

Cited by 47 publications

(5 citation statements)

References 42 publications

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“…Up to this point, there's been no limitation on the number of messages the sender can use. Following the revelation principle, we can view each message as an action recommendation, as each message induces a posterior belief of the receiver, which leads to a certain action (Kamenica and Gentzkow 2011; Dughmi and Xu 2016). Thus the number of messages can be set equal to the number of actions without harming the sender's interest, i.e., |M | = d. In other words, given any messaging scheme, we can always construct an equivalent scheme π with the message set M A = {m a : a ∈ A}, where each message m a corresponds to an action recommendation a ∈ A.…”

Section: Optimization Problem Formulationmentioning

confidence: 99%

A Fast Algorithm for k-Memory Messaging Scheme Design in Dynamic Environments with Uncertainty

Fan,

Shen

2024

ICAPS

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We study the problem of designing the optimal k-memory messaging scheme in a dynamic environment. Specifically, a sender, who can perfectly observe the state of a dynamic environment but cannot take actions, aims to persuade an uninformed, far-sighted receiver to take actions to maximize the long-term utility of the sender, by sending messages. We focus on k-memory messaging schemes, i.e., at each time step, the sender's messaging scheme depends on information from the previous k steps. After receiving a message, the self-interested receiver derives a posterior belief and takes action. The immediate reward of each player can be unaligned, thus the sender needs to ensure persuasiveness when designing the messaging scheme. We first formulate this problem as a bi-linear program. Then we show that there are infinitely many non-trivial persuasive messaging schemes for any problem instance. Moreover, we show that when the sender uses a k-memory messaging scheme, the optimal strategy for the receiver is also a k-memory strategy. We propose a fast heuristic algorithm for this problem and show that it can be extended to the setting where the sender has threat ability. We experimentally evaluate our algorithm, comparing it with the solution obtained by the Gurobi solver, in terms of performance and running time, in both settings. Extensive experimental results show that our algorithm outperforms the solution in running time, yet achieves comparable performance.

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Section: Optimization Problem Formulationmentioning

confidence: 99%

A Fast Algorithm for k-Memory Messaging Scheme Design in Dynamic Environments with Uncertainty

Fan,

Shen

2024

ICAPS

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“…Dughmi and Xu [23] analyze for the first time Bayesian persuasion from a computational perspective, focusing on the single receiver case. In [18], Arieli and Babichenko introduce the model of persuasion with multiple receivers and without inter-agent externalities, with a focus on private Bayesian persuasion.…”

Section: Context: Persuasion With Multiple Receiversmentioning

confidence: 99%

Public Bayesian Persuasion: Being Almost Optimal and Almost Persuasive

2023

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We study algorithmic Bayesian persuasion problems in which the principal (a.k.a. the sender) has to persuade multiple agents (a.k.a. receivers) by using public communication channels. Specifically, our model follows the multi-receiver model with no inter-agent externalities introduced by Arieli and Babichenko (J Econ Theory 182:185–217, 2019). It is known that the problem of computing a sender-optimal public persuasive signaling scheme is not approximable even in simple settings. Therefore, prior works usually focus on determining restricted classes of the problem for which efficient approximation is possible. Typically, positive results in this space amounts to finding bi-criteria approximation algorithms yielding an almost optimal and almost persuasive solution in polynomial time. In this paper, we take a different perspective and study the persuasion problem in the general setting where the space of the states of nature, the action space of the receivers, and the utility function of the sender can be arbitrary. We fully characterize the computational complexity of computing a bi-criteria approximation of an optimal public signaling scheme in such settings. In particular, we show that, assuming the Exponential Time Hypothesis, solving this problem requires at least a quasi-polynomial number of steps even in instances with simple utility functions and binary action spaces such as an election with the k-voting rule. 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, under mild assumptions, yields a QPTAS.

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“…Applications to auctions (Emek et al, 2014) and voting (Alonso and C Âmara, 2016) are considered. The computational complexity of Bayesian persuasion is determined (Dughmi and Xu, 2016). Interested readers can refer to the surveys by Dughmi (2017), Kamenica (2019), and Bergemann and Morris (2019) for excellent overviews of the literature.…”

Section: Related Workmentioning

confidence: 99%

Persuading a Behavioral Agent: Approximately Best Responding and Learning

Lin¹

2023

Preprint

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The classic Bayesian persuasion model assumes a Bayesian and best-responding receiver. We study a relaxation of the Bayesian persuasion model where the receiver can approximately best respond to the sender's signaling scheme. We show that, under natural assumptions, (1) the sender can find a signaling scheme that guarantees itself an expected utility almost as good as its optimal utility in the classic model, no matter what approximately best-responding strategy the receiver uses; (2) on the other hand, there is no signaling scheme that gives the sender much more utility than its optimal utility in the classic model, even if the receiver uses the approximately best-responding strategy that is best for the sender. Together, (1) and ( 2) imply that the approximately best-responding behavior of the receiver does not affect the sender's maximal achievable utility a lot in the Bayesian persuasion problem. The proofs of both results rely on the idea of robustification of a Bayesian persuasion scheme: given a pair of the sender's signaling scheme and the receiver's strategy, we can construct another signaling scheme such that the receiver prefers to use that strategy in the new scheme more than in the original scheme, and the two schemes give the sender similar utilities. As an application of our main result (1), we show that, in a repeated Bayesian persuasion model where the receiver learns to respond to the sender by some algorithms, the sender can do almost as well as in the classic model. Interestingly, unlike (2), with a learning receiver the sender can sometimes do much better than in the classic model.

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Algorithmic Bayesian persuasion

Cited by 47 publications

References 42 publications

A Fast Algorithm for k-Memory Messaging Scheme Design in Dynamic Environments with Uncertainty

A Fast Algorithm for k-Memory Messaging Scheme Design in Dynamic Environments with Uncertainty

Public Bayesian Persuasion: Being Almost Optimal and Almost Persuasive

Persuading a Behavioral Agent: Approximately Best Responding and Learning

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