Markovian Persuasion with Two States

TL;DR

This paper studies optimal information transmission over time in a Markovian binary state model, revealing that the sender's best strategy involves sometimes withholding information or splitting beliefs, especially as communication becomes continuous.

Contribution

It characterizes the sender's optimal strategy in a continuous-time limit, showing it is non-myopic and involves belief splitting or withholding based on the agent's beliefs.

Findings

Optimal strategies depend on the agent's current belief.

Sometimes no information is revealed to influence actions.

Belief splitting is used as a strategic tool.

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. The optimal strategy is not myopic. Depending on the agent's beliefs, sometimes no information is revealed, and sometimes the agent's belief is split into two well-chosen posterior beliefs.