Hierarchical cheap talk

We investigate situations in which agents can communicate to each other only through a chain of intermediators, for example because they have to obey institutionalized communication protocols. We assume that all involved in the communication are strategic, and might want to influence the action taken by the final receiver. The set of pure strategy equilibrium outcomes is simple to characterize, monotonic in each intermediator's bias, does not depend on the order of intermediators, and intermediation in these equilibria cannot improve information transmission. However, none of these conclusions hold for mixed equilibria. We provide a partial characterization of mixed equilibria, and offer an economically relevant sufficient condition for every equilibrium to be outcome-equivalent to a pure equilibrium and hence the simple characterization and comparative statics results to hold for the set of all equilibria.