On the (im)possibility of improving upon the student-proposing deferred acceptance mechanism

This paper studies a general school choice problem with or without outside options. The Gale-Shapley student-proposing deferred acceptance mechanism (DA) has played a central role not only in theory but also in important practical applications. We show that in problems where some students cannot credibly submit a single school as the only acceptable option, it is possible to improve upon DA without sacrificing strategyproofness. On the other hand, in unrestricted problems where no outside options necessarily exist, it is not possible to improve upon DA via a strategy-proof mechanism.