Stability in Many-to-One Matching with Couples having Responsive Preferences

TL;DR

This paper investigates the existence of stable matchings in many-to-one markets with couples having responsive preferences, identifying conditions that guarantee stability across all preference profiles.

Contribution

It establishes necessary and sufficient conditions on couples' and institutions' preferences to ensure stable matchings always exist in such markets.

Findings

Stable matchings may not exist without specific preference conditions.

Conditions on couples' preferences guarantee stability for all institution preferences.

Conditions on institutions' preferences guarantee stability for all couples' preferences.

Abstract

This paper studies matching markets where institutions are matched with possibly more than one individual. The matching market contains some couples who view the pair of jobs as complements. First, we show by means of an example that a stable matching may fail to exist even when both couples and institutions have responsive preferences. Next, we provide conditions on couples' preferences that are necessary and sufficient to ensure a stable matching for every preference profile where institutions may have any responsive preference. Finally, we do the same with respect to institutions' preferences, that is, we provide conditions on institutions' preferences that are necessary and sufficient to ensure a stable matching for every preference profile where couples may have any responsive preference.