On Cheap Talk and Burned Money

Austen-Smith and Banks (Journal of Economic Theory, 2000) study how money burning can expand the set of pure cheap talk equilibria of Crawford and Sobel (Econometrica, 1982). This paper proves their conjecture on continuity of the equilibrium set as the upper bound on burned money shrinks to 0. I then study how the set of equilibria can be reflned using forward-induction. While standard criteria such as D1 or divinity are shown to be relatively inefiective, a stronger version, the monotonic D1 criterion, is quite useful. I characterize the class of such equilibria for an arbitrary amount of available burned money, and prove that as the upper bound on burned money shrinks to 0, the set converges uniquely to the most informative equilibrium of the pure cheap talk game (under a standard regularity condition). I also identify an error in Austen-Smith and Banks’ main Theorem, and provide a variant that preserves some of the important implications.