Dynamic Cheap Talk without Feedback

TL;DR

This paper analyzes a dynamic sender-receiver game where the sender observes a Markovian state without feedback, demonstrating how dynamic interaction can replicate commitment-like outcomes and achieve Bayesian persuasion payoffs.

Contribution

It shows that equilibrium payoffs in a persuasion model with partial commitment can be achieved in a dynamic game without feedback, extending the understanding of commitment in dynamic communication.

Findings

Any equilibrium payoff with partial commitment can be achieved dynamically.

Convex combinations of such payoffs are also sustainable.

State-independent sender payoffs match Bayesian persuasion outcomes.

Abstract

We study a dynamic sender-receiver game in which the sender observes a state evolving according to a Markov chain but does not observe the receiver's action. Despite the absence of feedback, dynamic interaction partially restores commitment. We show that any equilibrium payoff of a persuasion model with partial commitment, where the sender can deviate to signaling policies that preserve the marginal distribution over messages, can be achieved as a uniform equilibrium payoff in the dynamic game. Moreover, any convex combination of such payoffs across message distributions can also be sustained. When the sender's payoff is state-independent, she achieves the Bayesian persuasion payoff.