Behavioral types and partially informed decision makers in communication games

This dissertation consists of two chapters on communication games.; The first chapter introduces two behavioral types into a model of strategic communication based on Crawford and Sobel (1982). With positive probability, the sender is an honest type who always tells the truth, and the receiver is a naive type who always follows whatever message is sent to her. We establish existence and uniqueness of monotonic equilibrium (a sequential equilibrium in which the sender's message strategy is non-decreasing in the state of the world) under certain assumptions. In this important class of equilibria, we find that only the most informative equilibrium in the C-S model is robust to the perturbation of the behavioral types. In a monotonic equilibrium, the dishonest sender always distorts the messages in the direction of his bias. If the message space is discrete and the dishonest sender has an upward bias, then his messages will cluster around the top few messages. Interestingly, the sophisticated receiver's strategy is not monotonic in the messages she receives even in a monotonic equilibrium. The existence of monotonic equilibrium may fail when the message space is a continuum. Following Manelli (1996), we show that adding incentive compatible communication (cheap-talk extension) restores existence.; The second chapter incorporates partially informed decision makers into communication games. We analyze three extensive form games in which the expert and the decision maker (DM) each privately observe a signal about the state of the world. In game 1, the DM reveals her private signal to the expert before the expert reports to her. In game 2, the DM keeps her signal private. In game 3, the DM strategically communicates to the expert before the expert reports to her. We find that the DM's expected equilibrium payoff is not monotonically increasing in the accuracy of her private signal because the expert may reveal less information when facing a well-informed DM. Whether the DM extracts more information from the expert in game 1 or in game 2 depends on the parameters. Allowing the DM to communicate strategically to the expert first does not help her extract more information.