Not so cheap talk: costly and discrete communication

We model an interaction between an informed sender and an uninformed receiver. As in the classic cheap talk setup, the informed player sends a message to an uninformed receiver who is to take an action which affects the payoffs of both players. However, in our model, the sender can communicate only through the use of discrete messages which are ordered by the cost incurred by the sender. We characterize the resulting equilibria without refining out‐of‐equilibrium beliefs. Subsequently, we apply an adapted version of the no incentive to separate (NITS) condition to our model. We show that if the sender and receiver have aligned preferences regarding the action of the receiver, then NITS only admits the equilibrium with the largest possible number of induced actions. When the preferences between players are not aligned, we show that NITS does not guarantee uniqueness, and we provide an example where an increase in communication costs can improve communication. As we show, this improvement can occur to such an extent that the equilibrium outperforms the Goltsman et al. (2009) upper bound for receiver’s payoffs in mediated communication.