We propose an assignment model in which positions along a hierarchy are attributed to individuals depending on their characteristics. Our theoretical framework can be used to study differences in assignment and outcomes across groups and we show how it can motivate decomposition and...

In centralized school admissions systems, rationing at oversubscribed schools often uses lotteries in addition to preferences. This partly random assignment is used by empirical researchers to identify the effect of entering a school on outcomes like test scores. This paper formally studies if...

We fully solve an assignment problem with heterogeneous firms and multiple heterogeneous workers whose skills are imperfect substitutes, that is, when production is submodular. We show that sorting is neither positive nor negative and is characterized sufficiently by two regions. In the first...