College Admissions with Scholarship

Merit-based scholarships are widely used to attract high-achieving students, but do they guarantee an improvement in the merit of a university's student pool? We study this question in centralized college admissions using a matching with contracts framework. We first introduce the scholarship choice rule, which processes scholarship levels from highest to lowest and selects the highest-merit students at each level. We show that scholarship feasibility, scholarship maximality, and no justified envy uniquely characterize this rule. We further characterize the student-proposing deferred-acceptance mechanism based on this rule as the unique mechanism, up to outcome equivalence, satisfying the extensions of the three axioms, together with individual rationality, and strategy-proofness. We then study the welfare effects of scholarship provision. In general matching markets, a university may be matched with lower-merit students after introducing a scholarship. Finally, when all schools use the scholarship choice rule and every student is eligible for every scholarship level a school offers, we show that a common merit ranking is necessary and sufficient for scholarship provision to guarantee, for every student-preference profile satisfying within-school monotonicity, a weak improvement in the scholarship-providing school's student pool.