The College Admissions Problem Reconsidered

This paper revisits the college admissions problem and studies the efficiency, incentive, and monotonicity for colleges. We show that max-min criterion that is stronger than substitutability, together with the quota-saturability that requires having enough acceptable applicants, guarantees weak Pareto efficiency and strategy-proofness for colleges under the colleges-proposing deferred acceptance algorithm. Moreover, we introduce a new notion of max-min criterion, called W-max-min criterion, which together with the quota-saturability condition, ensures that the colleges-proposing deferred acceptance algorithm is not only weakly Pareto efficient and strategy-proof, but also monotone for colleges.