Continuous-time persuasion by filtering

René Aïd (), Ofelia Bonesini (), Giorgia Callegaro () and Luciano Campi ()
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René Aïd: LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Ofelia Bonesini: LSE - Department Mathematics [London] - LSE - London School of Economics and Political Science
Giorgia Callegaro: Dipartimento di Matematica [Padova] - Unipd - Università degli Studi di Padova = University of Padua
Luciano Campi: Department of Mathematics "Federigo Enriques" - UNIMI - Università degli Studi di Milano = University of Milan

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Abstract: We frame dynamic persuasion in a partial observation stochastic control Leader-Follower game with an ergodic criterion. The Receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the Receiver through a device designed by the Sender that generates the observation process. The commitment of the Sender is enforced. We develop this approach in the case where all dynamics are linear and the preferences of the Receiver are linear-quadratic. We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the Receiver's value function. An extension to the case of persuasion of a mean field of interacting Receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that information provision is a substitute for best-in-class objective.

Keywords: persuasion; filtering; ergodic control; Stackelberg games; mean field games; smart meters; carbon footprint. JEL classification: C61; C73; D82; D83; Q51. MSC 2020 classification: 93E11; 91A15; 91A16; 91B76; Optimization and Control (math.OC); Probability (math.PR); FOS: Mathematics (search for similar items in EconPapers)
Date: 2025-03-28
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