Information structures in college admissions

We study the role of priority information structures in a simple college admissions model where a continuum of students share a common preference. Each student with partial information about the priority order strategically applies to a single school, which then admits students based on the realized priority order. The first main theorem characterizes equilibrium student distributions across schools. A simple class of disclosure rules, cutoff signals, can implement any equilibrium distribution and generate ex-ante fair allocations that are also the closest to being ex-post fair among distributions achieving the same outcome. As an application, we examine an information design problem. The second main theorem shows that each equilibrium distribution is implementable as a unique equilibrium.