Informationally Robust Cheap-Talk

TL;DR

This paper analyzes the robustness of cheap-talk equilibria when receivers have infinitesimal private information, identifying conditions under which sender-optimal equilibria remain stable and characterizing optimal sender utility.

Contribution

It provides a complete characterization of robust cheap-talk equilibria under private information and determines the conditions for the optimal sender utility in such settings.

Findings

Sender-optimal equilibrium is robust if it reveals no information or fully reveals one state.

The paper characterizes actions played with positive probability in any robust equilibrium.

It derives bounds for the sender's utility under general private information.

Abstract

We study the robustness of cheap-talk equilibria to infinitesimal private information of the receiver in a model with a binary state-space and state-independent sender-preferences. We show that the sender-optimal equilibrium is robust if and only if this equilibrium either reveals no information to the receiver or fully reveals one of the states with positive probability. We then characterize the actions that can be played with positive probability in any robust equilibrium. Finally, we fully characterize the optimal sender-utility under binary receiver's private information, and provide bounds for the optimal sender-utility under general private information.