Strategic Simplicity in Multidimensional Screening

We study strategically simple mechanisms for a class of multidimensional screening problems that arise frequently in applications: a designer must allocate a set of heterogeneous items among agents, while each agent has the right to demand a status-quo assignment. We first model strategic simplicity via the notion of obvious strategy-proofness (OSP). Static OSP mechanisms take a simple form in which agents choose from a diverse menu of narrowly defined veto rights: each agent chooses from a menu of one-dimensional sets in which their assignment can lie, and these sets must represent sufficiently differentiated directions of trade away from the status quo. We call these polarized-ray mechanisms. For general extensive-form games, the characterization of OSP mechanisms preserves much of the polarized-ray structure from the static case. We then consider a more demanding notion of strong obvious strategy-proofness, and show that such mechanisms essentially reduce to sequential implementation of polarized-ray mechanisms. We characterize the convex structure of polarized-ray mechanisms and develop tools for optimizing over this set. Finally, we examine the potential of this simple class of mechanisms as a practical market-design tool and provide quantitative evidence of their performance in two empirical applications: the assignment of Child Protective Services investigations to caseworkers and the assignment of misdemeanor cases to prosecutors.