Not so cheap talk: a model of advice with communication costs

We model a game similar to the interaction between an academic advisor and advisee. Like the classic cheap talk setup, an informed player sends information to an uninformed receiver who is to take an action which affects the payoffs of both sender and receiver. However, unlike the classic cheap talk setup, the preferences regarding the receiver's actions are identical for both sender and receiver. Additionally, the sender incurs a communication cost which is increasing in the complexity of the message sent. We characterize the resulting equilibria. Under an additional out-of-equilibrium condition (Condition L), if preferences for sender and receiver are identical then the only equilibria are the most informative, feasible ones. A similar result appears in Chen, Kartik and Sobel (2008) when their No Incentive to Separate (NITS) condition is applied to the case where communication is costless but preferences diverge. Additionally, we model the competency of the advisee by the probability that the action is selected by mistake. We show that the informativeness of the sender is decreasing in the likelihood of the mistake. When the preferences between players diverge and when there are communication costs, we are not guaranteed uniqueness and we provide an example where an increase in communication costs can improve communication.