The Core of School Choice Problems
28 Pages Posted: 16 Apr 2020 Last revised: 1 Dec 2022
Date Written: April 2, 2020
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 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. We also propose a natural refinement of the core and show that it is equivalent to the concept of priority-efficiency proposed by Reny (2022).
Keywords: Core, Deferred acceptance algorithm, Pareto efficiency, school choice, stability, top trading cycles
JEL Classification: C78; D61; D78; I20
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