How to talk to multiple audiences

We analyze the performance of various communication protocols in a generalization of the Crawford-Sobel (1982) model of cheap talk that allows for multiple receivers. We find that the sender prefers communicating by private messages if the receivers' average bias is high, and by public messages if the receivers' average bias is low and the receivers are sufficiently polarized. When both public and private messages are allowed, the sender can combine the commitment provided by public communication with the flexibility of private communication and transmit more information to the receivers than under either private or public communication scenarios. When the players can communicate through a mediator and the receivers are biased in the same direction, it is optimal for the sender to communicate with the receivers through independent private noisy communication channels.