Persuasion with limited communication capacity

We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on the payoffs the persuader can secure by communicating through...

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Bibliographic Details
Published in:Journal of economic theory Vol. 184; p. 104940
Main Authors: Le Treust, Maël, Tomala, Tristan
Format: Journal Article
Language:English
Published: Elsevier Inc 01.11.2019
Elsevier
Subjects:
Bayesian persuasion
Communication channel
Computer Science
Computer Science and Game Theory
Humanities and Social Sciences
Information Theory
Library and information sciences
Mutual information
Bayesian persuasion
Communication channel
D83
Mutual information
C72
D82
communication channel
mutual information
ISSN:0022-0531, 1095-7235
Online Access:Get full text
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Summary:We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel that has a fixed and limited number of messages and is subject to exogenous noise. We provide an upper bound on the payoffs the persuader can secure by communicating through the channel. We also show that the bound is tight, i.e., if the persuasion problem consists of a large number of independent copies of the same base problem, then the persuader can achieve this bound arbitrarily closely by using strategies that tie all the problems together. We characterize this optimal payoff as a function of the information-theoretic capacity of the communication channel.
ISSN:0022-0531
1095-7235
DOI:10.1016/j.jet.2019.104940