We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agents' preferences. We introduce a method that finds all core matchings, if any exist. The… (More)
Controlled choice over public schools attempts giving parents selection options while maintaining diversity of different student types. In practice, diversity constraints are often enforced by setting hard upper bounds and hard lower bounds for each student type. We demonstrate that, with hard bounds, there might not exist assignments that satisfy standard… (More)
We define the median stable matching for two-sided matching markets with wages and prove constructively that it exists. Michael Ostrovsky, the editor and two anonymous referees for helpful suggestions. We also thank Federico Echenique for detailed comments on an earlier draft.