Markov Persuasion Processes: How to Persuade Multiple Agents From Scratch

Francesco Bacchiocchi, Francesco Emanuele Stradi, Matteo Castiglioni, Nicola Gatti, Alberto Marchesi

Keywords: Bayesian Persuasion, Markov Persuasion Process, Online Learning

Abstract: In Bayesian persuasion, an informed sender strategically discloses information to a receiver so as to persuade them to undertake desirable actions. Recently, Markov persuasion processes (MPPs) have been introduced to capture sequential scenarios where a sender faces a stream of myopic receivers in a Markovian environment. The MPPs studied so far in the literature suffer from issues that prevent them from being fully operational in practice, e.g., they assume that the sender knows receivers’ rewards. We fix such issues by addressing MPPs where the sender has no knowledge about the environment. We design a learning algorithm for the sender, working with partial feedback. We prove that its regret with respect to an optimal information-disclosure policy grows sublinearly in the number of episodes, as it is the case for the loss in persuasiveness cumulated while learning. Moreover, we provide a lower bound for our setting matching the guarantees of our algorithm.

Submission Number: 44