Toxic Types and Infectious Communication Breakdown

We introduce a new reason for why an informed sender may not be able to communicate(via cheap talk) his private information to an uninformed receiver. Our framework has two novel features: (i) conditional on interacting, both parties agree on the optimal action to take given the sender’s information, and (ii) there are some sender types (the “toxic†types) with which the receiver prefers not to interact. Our main result establishes that for a broad class of preferences, any interval equilibrium (where each message is associated with an interval of types) induces only finitely many actions in the support of the receiver’s strategy. For a canonical class of preferences with uniformly distributed types, we characterize the Pareto efficient(interval) equilibria and illustrate how communication is adversely affected even with a small set of toxic types. In addition, we show that introducing a second stage in which the receiver gets a noisy signal on the sender type can have a dramatic effect on the first-stage communication.