Data and Code for: Crowding in School Choice

We consider the market design problem of matching students to schools in the presence of crowding effects. These effects are salient in parents' decision making and the empirical literature; however, they cause difficulties in the design of satisfactory mechanisms and, as such, are not currently considered. We propose a new framework and an equilibrium notion that accommodates crowding, no-envy, and respect for priorities. The equilibrium has a student-optimal element that induces an incentive compatible mechanism and is implementable via a novel algorithm. Moreover, analogs of fundamental structural results of the matching literature---the Rural Hospitals Theorem, welfare lattice, etc.---survive.