Markovian persuasion with two states

Abstract

This paper addresses the question of how to best communicate information over time in order to influence an agent's belief and induced actions in a model with a binary state of the world that evolves according to a Markov process, and with a finite number of actions. We characterize the sender's optimal message strategy in the limit, as the length of each period decreases to zero. We show that the limit optimal strategy is myopic for beliefs smaller than the invariant distribution of the underlying Markov process. For beliefs larger than the invariant distribution, the optimal policy is more elaborate and involves both silence and splitting of the receiver's beliefs; it is not myopic.