Dynamic Cheap Talk without Feedback
arXiv:2604.26443
The paper analyzes a dynamic sender‑receiver game where the sender observes a Markovian state but cannot see the receiver’s actions, showing that despite the lack of feedback the sender can achieve equilibrium payoffs equivalent to those in a partial‑commitment persuasion model, and when the sender’s payoff is state‑independent she can attain the Bayesian persuasion payoff.
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.