Evanston: Northwestern Univ., Kellogg Graduate School of Management, Center for Mathematical Studies in Economics and Management Science
We explore when it is optimal for senders to commit to signal structures which induce the receiver to take higher actions when the underlying state is higher and the preferences of the receiver satisfy strategic complementarity conditions. Building on the literature on monotone comparative statics, we provide sufficient conditions for the sender's optimal signal structure consists of a monotone partition of the state space, and characterize the boundary conditions. When the action space is binary, it is optimal to use a monotone partition if the sender's preferences are supermodular in the action and the state. In the case of a continuum of actions, though, one must take into account the additional effect that altering the receiver's posteriors also affect her choice. We provide a new single-crossing condition that takes account of this effect, and guarantees monotonicity given appropriate conditions on the cost of implementing the signal structure. If it is costless to provide information, it will be optimal for the sender to reveal all information. Applications are provided to preference disagreement with biases, as well as to expected revenue maximization.
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