Efficient Matching in the School Choice Problem

Abstract

Stable matchings in school choice needn’t be Pareto efficient and can leave thousands of students worse off than necessary. Call a matching μ priority-neutral if no matching can make any student whose priority is violated by μ better off without violating the priority of some student who is made worse off. Call a matching priority-efficient if it is priority-neutral and Pareto efficient. We show that there is a unique priority-efficient matching and that it dominates every priority-neutral matching and every stable matching. Moreover, truth-telling is a maxmin optimal strategy for every student in the mechanism that selects the priority-efficient matching. (JEL C78, I21, I28)