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. The messages are ordered by the cost incurred by the sender upon its transmission. We characterize the resulting equilibria under a weak out-of-equilibrium condition. We apply the stronger no incentive to seperate (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 most informative equilibrium. 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 an equilibrium outperforms the Goltsman et. al. (2009) upper bound for payoffs in mediated communication.