[UTMD-073] Double Stability in Two-Sided Matching: Priority and Preference in Harmony (by Yuanju Fang, Yosuke Yasuda)

Yuanju Fang, Yosuke Yasuda

In two-sided matching problems, there can be ambiguity regarding whether institutions such as schools and daycares should be treated as agents who can make decisions, objects to be assigned, or both. To address this, we consider an extended college admissions model that incorporates a common priority order, often determined by external criteria such as exam scores or institutional rules, alongside the preferences of students and colleges. We define a matching as double stable if it satisfies priority stability and preference stability simultaneously. Our main finding establishes that a double stable matching exists if and only if the resulting outcome of the serial dictatorship mechanism coincides with that of the student-proposing deferred acceptance mechanism.