Constrained school choice

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 assignment 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 of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guarantee stability. This stands in sharp contrast with the Boston mechanism which yields stable Nash equilibrium outcomes. Hence, the transition to any of the two mechanisms while keeping a restriction on the submittable preference lists may cause lower priority students to occupy more preferred schools. JEL classification: C72, C78, D78, I20