Screening Inattentive Agents

Abstract: Information plays a crucial role in mechanism design problems. A  potential complication is that this information may endogenously and flexibly depend on what options they are offered. I model this by considering an optimal mechanism design problem in which a principal screens agents with uncertain value. The agent is inattentive regarding their true value, and decides how to optimally acquire information in response to the offered mechanism. I show that any implementable mechanism is characterized by a non-participation belief, which in turn determines the beliefs and prices for every possible probability of allocation (including those not chosen). For every possible non-participation belief, the mechanism design problem then reduces to one of Bayesian persuasion. The optimal mechanism is then implicitly determined by choosing the optimal non-participation belief. I provide results characterizing optimal mechanisms in both the single- and multiple-agent cases.