The Art of Brevity

We analyze a class of sender-receiver games with quadratic payo¤s, which includes the communication games in Alonso, Dessein and Matouschek (2008) and Rantakari (2008) as special cases, for which the receivers maximum expected payo¤when players have access to arbitrary, mediated communication protocols is attained in one-round of face-to-face, unmediated cheap talk. This result is based on the existence for these games of a communication equilibrium with an in\u85nite number of partitions of the state space. We provide explicit expressions for the maximum expected payo ¤ of the receiver, and illustrate its use by deriving new comparative statics of the quality of optimal communication. For instance, a shift in the underlying uncertainty that reduces expected conict can worsen the quality of communication. JEL classi\u85cation: C72, D70, D83