Two stage mechanisms for matching students and supervisors

The Deferred Acceptance (DA) algorithm ensures stable matchings but is often impractical in large university settings. Many institutions therefore use a two-stage approach: supervisors are grouped by topic, groups and students rank each other, and DA is applied first between students and groups, then within each group between students and supervisors. We show that such two-stage bundling mechanisms guarantee overall stability if and only if students have lexicographic preferences and supervisors share identical preferences within their groups.