Finding a Stable Matching under Type-Specific Minimum Quotas
In two-sided matching with minimum and maximum type-specific quotas, there may not exist a stable (i.e., fair and non-wasteful) assignment (Ehlers et al., 2014). This paper investigates the structure of schools' priority rankings which guarantees stability. First, we show that there always exists a fair and non-wasteful assignment if for each type of students, any two schools have common priority rankings over a certain number of bottom students. Next, we show that this condition also characterizes the maximal domain of two schools' priority rankings over same type students to guarantee the existence of stable assignments. To prove the existence theorem, we propose a new mechanism Deferred Acceptance with Precedence Lists (DAPL), which is feasible, non-wasteful and strategy-proof for any priority rankings. DAPL always satisfies strict PL-fairness, which is weaker than fairness, and satisfies fairness under our sufficient conditions.