Strategy-proof improvements upon deferred acceptance: A maximal domain for possibility

In one-sided matching/assignment problems, an important debate centers around whether it is possible to improve upon the Gale-Shapley student-proposing deferred acceptance mechanism (DA) via alternative strategy-proof mechanisms. In unrestricted preference domains, no strategy-proof mechanism Pareto improves upon DA whether students have outside options or not. When standard exogenous outside options, e.g., private school, do not necessarily exist, we show that endogenous outside options, i.e., problem-specific schools that could always accept a deviating student, arise and the impossibility of obtaining a strategy-proof improvements over DA prevails. It is, however, possible to construct natural subdomains allowing for positive results, where some students' preferences are in part induced by an exogenous hierarchy of quality tiers. We then identify maximal domains on which it is possible to improve upon DA without sacrificing strategy-proofness. This result may help better assess the underpinnings of the three-way tension among efficiency, individual rationality/stability, and strategy-proofness in matching problems.