Communication with Multiple Senders

Abstract: This paper analyzes a cheap talk model with one receiver and multiple senders. Each sender observes a noisy signal regarding an unknown state of the world. Existing literature (e.g., Levit and Malenko, 2011; Battaglini, 2017) focuses on scenarios where the receiver and senders have aligned preferences in each state. We further explore situations with disagreement states where the receiver and the senders have misaligned preferences. We first show that, when the number of senders grows large, each sender's message must convey almost no information to the receiver. Furthermore, we identify a discontinuity in information transmission: with moderate conflict between the receiver and the senders, introducing an arbitrarily small probability of disagreement states causes complete unraveling, contrary to complete information transmission predicted by the literature. Finally, we demonstrate that the receiver cannot fully learn the state even when receiving messages from arbitrarily many senders.