Persuasion with limited communication capacity

Mael Le Treust (1) , Tristan Tomala (2)

1 ETIS - UMR 8051 - Equipes Traitement de l'Information et Systèmes
2 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC

We consider a Bayesian persuasion problem where the persuader and the decision maker communicate through an imperfect channel which has a fixed and limited number of messages and is subject to exogenous noise. Imperfect communication entails a loss of payoff for the persuader. We establish an upper bound on the payoffs the persuader can secure by communicating through the channel. We also show that the bound is tight: 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 which tie all the problems together. We characterize this optimal payoff as a function of the information-theoretic capacity of the communication channel.

Mots clés: Bayesian persuasion; communication channel; mutual information

Domaines: Sciences de l'information et de la communication; Informatique et théorie des jeux [cs.GT]; Théorie de l'information [cs.IT]

Mael Le Treust, Tristan Tomala. Persuasion with limited communication capacity. Journal of Economic Theory, 2019. ⟨hal-01633656v3⟩