Hierarchical cheap talk∗

We investigate situations in which agents can only communicate to each other 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 hold for the set of all equilibria. ∗We thank Joel Sobel for an extensive discussion about the paper, and Michihiro Kandori, Bart Lipman, Shih-En Lu, Marco Ottaviani, three anonymous referees, and seminar participants at Harvard University, Stanford University, UCLA, CalTech, UC SanDiego, UC Davis, the 20th Stony Brook Game Theory Conference, and the 2009 Far East and South Asia Meetings of the Econometric Society for useful comments. †Ambrus: Department of Economics, Harvard University, Cambridge, MA 02138, email: [email protected]. Azevedo: Department of Economics, Harvard University, Cambridge, MA 02138, e-mail: [email protected]. Kamada: Department of Economics, Harvard University, Cambridge, MA 02138, e-mail: [email protected].