In the classic College Admissions problem, there are $m$ colleges and $n$ students. The colleges have a preference over the students and the students have preferences over the colleges. The students do not care who are the other students admitted to the college. The Gale-Shapley algorithm guarantees a stable matching in this case.
Now suppose I introduce a form of externality where a student's utility depends not only on the college he/she is admitted to, but also on who are the other students who are admitted to that college. What is the definition of stability in this case? Does a stable allocation always exist here? How to find one if it does?