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...

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and...

We experimentally study the Gale and Shapley (1962) mechanism, which is utilized in a wide set of applications, most prominently the National Resident Match- ing Program (NRMP). Several insights come out of our analysis. First, only 48% of our observed outcomes are stable, and among those a...