The core of school choice problems

We propose a notion of core for school choice (i.e., priority-based allocation) 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 student in the coalition from her assigned school. 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 all assignments in the core are Pareto efficient, and the assignment produced by Kesten’s efficiency-adjusted deferred acceptance algorithm is always in the core. We also propose a natural refinement of the core and show that it is equivalent to the concept of priority-efficiency proposed by Reny (Am Econ Rev 112:2025–2043, 2022).