Constrained School Choice

Abstract

Recently, several school districts in the US have adopted or consider adopting the
Student-Optimal Stable mechanism or the Top Trading Cycles mechanism to assign
children to public schools. There is evidence that for school districts that employ
(variants of ) the so-called Boston mechanism the transition would lead to efficiency
gains. The first two mechanisms are strategy-proof, but in practice student assign-
ment procedures typically impede a student to submit a preference list that contains
all his acceptable schools. We study the preference revelation game where students
can only declare up to a fixed number of schools to be acceptable. We focus on the
stability and efficiency of the Nash equilibrium outcomes. Our main results identify
rather stringent necessary and sufficient conditions on the priorities to guarantee
stability or efficiency of either of the two mechanisms. This stands in sharp contrast
with the Boston mechanism which has been abandoned in many US school districts
but nevertheless yields stable Nash equilibrium outcomes.

JEL classification: C72, C78, D78, I20

Keywords: school choice, matching, Nash equilibrium, stability, efficiency, Gale-
Shapley deferred acceptance algorithm, top trading cycles, Boston mechanism, acyclic
priority structure

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