Markovian Persuasion

TL;DR

This paper extends Bayesian persuasion to a dynamic setting where the state evolves as a Markov process, analyzing optimal disclosure strategies and their long-term implications under various discount factors.

Contribution

It introduces a dynamic Markovian model of persuasion and characterizes optimal strategies and asymptotic values in this setting.

Findings

Optimal disclosure balances immediate payoff and future belief updates.

Asymptotic value can reach the maximal possible under certain conditions.

Different discount factors significantly influence the optimal strategies.

Abstract

In the classical Bayesian persuasion model an informed player and an uninformed one engage in a static interaction. The informed player, the sender, knows the state of nature, while the uninformed one, the receiver, does not. The informed player partially shares his private information with the receiver and the latter then, based on her belief about the state, takes an action. This action determines, together with the state of nature, the utility of both players. We consider a dynamic Bayesian persuasion situation where the state of nature evolves according to a Markovian law. In this repeated persuasion model an optimal disclosure strategy of the sender should, at any period, balance between getting high stage payoff and future implications on the receivers' beliefs. We discuss optimal strategies under different discount factors and characterize when the asymptotic value achieves the maximal value possible.