Cheap talk by multiple speakers in the presence of network externalities

The authors develop a model of cheap talk with multiple speakers in the presence of network externalities so that their utility functions are increasing in the network size. They first show that if there is no noise in private information that each sender receives, the full information is revealed by the harshest cross-checking strategies, that is, strategies to punish the senders unless their messages exactly coincide. Then, the authors show that with even a small noise cross-checking strategies cannot induce full revelation if utility functions of senders are linear in the network size, while full revelation is possible if utility functions are strictly concave. They find a sufficient condition for the existence of a fully revealing equilibrium which is supported by the cross-checking strategy with a positive confidence interval independent of each sender's private information.