Robustness of full revelation in multisender cheap talk

This paper studies information transmission in a two‐sender, multidimensional cheap talk setting where there are exogenous constraints on the (convex) feasible set of policies for the receiver, and where the receiver is uncertain about both the directions and the magnitudes of the senders' bias vectors. With the supports of the biases represented by cones, we prove that whenever there exists an equilibrium that fully reveals the state, there exists a robust fully revealing equilibrium (FRE), i.e., one in which small deviations result in only small punishments. We provide a geometric condition—the local deterrence condition—that relates the cones of the biases to the frontier of the policy space, which is necessary and sufficient for the existence of a FRE. We also construct a specific policy rule for the receiver—the min rule—that supports a robust FRE whenever one exists.