Robust almost fully revealing equilibria in multi-sender cheap talk ∗

This paper shows that in multi-sender cheap talk games, if the state space is large enough, then there exist equilibria arbitrarily close to full revelation of the state that are robust to introducing a small amount of noise in the senders’ observations. The result holds irrespectively of the dimensionality of the state space, including for one-dimensional state spaces. We establish the result for both types of noise structures considered in the literature: (i) with small probability, the senders observe the realization of a random variable independent of the state (but with high probability they exactly observe the state); (ii) the senders observe the sum of the state and a noise term, the latter being independent across senders. In the equilibria that we propose, although a given equilibrium message of a sender is sent in various states far from each other, a given combination of messages by the senders identifies a small connected set of states with positive measure. Moreover, there is such a set of states associated with any combination of equilibrium messages, essentially eliminating out-of-equilibrium messages even in a game without noise.