Implementation of the Core in College Admissions Problems When Colleagues Matter

This paper presents mechanisms implementing the core correspondence of many-toone matching markets, such as college admissions problems, where the students have preferences over the other students who would attend the same college. With an unrestricted domain of preferences the non-emptiness of the core is not guaranteed. We present a sequential mechanism implementing the core without any restrictions on the preferences. We also show that simple two-stage mechanisms cannot be used to implement the core correspondence in subgame perfect Nash equilibrium without strong assumptions on agents’ preferences. JEL Classification Numbers: C78; D78.