Reputational cheap talk: influentialness and welfare

TL;DR

This paper analyzes how private communication influences decision-making, emphasizing the role of prior information and reputation in determining the effectiveness and welfare implications of informative equilibria.

Contribution

It characterizes the conditions for unique informative equilibria in signaling games and examines how prior information and reputation affect influence and welfare.

Findings

Informative equilibria can be noninfluential, offering no benefit to the receiver.

Sufficiently precise prior information restores influential communication.

The receiver's welfare depends on the quality of prior information and the sender's reputation.

Abstract

A sender communicates private information about a hidden state to a receiver who seeks to match his action to that state. The sender strives to appear informed at the receiver's expense. I characterize informative equilibria under a broad class of signal structures and show that, when they exist, they are essentially unique. I show that informative equilibria can be noninfluential, in which case the receiver does not benefit from communication and relies only on prior information. My main results identify a complementarity that sufficiently precise prior information helps restore influential communication and characterize how the receiver's welfare depends on the quality of prior information. I also characterize how the sender's initial reputation for being informed shapes these results.