The Core of School Choice Problems

We propose a notion of core for school choice problems. We say that a coalition of students is able to enforce a subassignment among them if, given their priorities at schools, other students together cannot exclude any of them from her assignment. An assignment is in the core if no coalition of students can enforce any subassignment among them that Pareto improves their assignments. We show that the core is always nonempty and all assignments in it are Pareto efficient. When the student-proposing deferred acceptance mechanism is a Pareto efficient mechanism, it always produces the unique assignment in the core