Need vs. merit: The large core of college admissions markets,

We study college admissions markets, where colleges offer multiple funding levels. Colleges wish to recruit the best-qualified students subject to budget and capacity constraints. Student-proposing deferred acceptance is stable and strategy-proof for students, but the set of stable allocations is large and the scope for manipulation by colleges is substantial, even in large markets. Under deferred acceptance, truthful colleges allocate funding based on merit. Successful
manipulations consider applicants’ outside options (specifically need)
when allocating funding. In Hungary, where the centralized clearinghouse uses deferred acceptance, choosing another stable allocation would increase the number of admitted students by at least 3%.