Robust Almost Fully Revealing Equilibria in Multi-Sender Cheap Talk
Attila Ambrus, Shih En Lu*
Last modified: 2013-04-18
Abstract
We show that in multi-sender cheap talk games where senders imperfectly observe the state, if the state space is large enough, then there exist equilibria arbitrarily close to full revelation of the state as the noise in the senders' observations vanishes. In the case of replacement noise, where the senders observe the true state with high probability, our equilibrium construction involves one round of communication. In the case of continuous noise, where senders observe a signal distributed according to a continuous distribution over an interval around the true state, our construction involves two rounds of communication. After the fi
rst round of communication, it becomes a common 1-belief between the senders that the state is in a small interval of the state space, even though before the communication, there is no nontrivial event that is a common p-belief between them for positive p. The results imply that when there are multiple experts from whom to solicit information, if the state space is large, then even when the state is observed imperfectly, there are communication equilibria that are strictly better for the principal than delegating the decision right to one of the experts.