The comparative statics of persuasion

Abstract

In the persuasion model, apart from a few special cases, comparative statics has been an open question. We answer it, delineating which shifts of the sender's interim payoff lead her optimally to choose a more informative signal. Our first theorem identifies a coarse notion of 'increased convexity' that we show characterises those shifts of the sender's interim payoff that lead her optimally to choose no less informative signals. To strengthen this conclusion to 'more informative' requires further assumptions: our second theorem identifies the necessary and sufficient condition on the sender's interim payoff, which strictly generalises the convex-concave ('S') shape commonly imposed in the literature. We identify conditions under which increased alignment of interests between sender and receiver leads to comparative statics, and study a number of applications.