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 whenever the sender can communicate informatively with both receivers by sending private messages, she can communicate informatively by sending public messages. In particular, it is possible that informative communication with one or both receivers is impossible in private, but possible in public. When the sender is allowed to send both public and private messages, it is possible for the sender to combine the commitment provided by public communication with the flexibility provided by 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. It is in general optimal to take advantage of pooling the sender's truthtelling constraints across the receivers when they are biased in the opposite directions.