[joint work with Ian Jewitt]
Abstract: We consider a class of persuasion games in which the sender has rank-dependent preferences. Like much of the recent Bayesian persuasion literature, we assume the receiver’s action depends only on her posterior expectation of a scalar state variable, and the sender may commit to a choice of experiment from a rich set (including, but not limited to, partitions). New to the literature, we consider settings in which the sender’s utility may be nonlinear in probabilities: this nonlinearity generates rank-dependent interests. The sender’s payoffs are otherwise linear in actions. In this environment, we geometrically characterize the sender’s optimal payoff from any information structure and identify the corresponding optimal experiment. For any prior distribution on a bounded support, we find that the sender’s optimal experiment must be monotone partitional. Moreover, our characterization admits a relatively simple analysis of comparative statics. We apply our analysis to several problems of economic interest: information design in auctions and elections, persuasion of an attention-constrained principal, and the design of investment projects when investors suffer from the `favourite-longshot’ bias.
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