Stability in Matching with Couples having Non-Responsive Preferences

We study many-to-one matching problems between institutions and individuals where an institution can possibly be matched to more than one individual. The matching market contains some couples, who view pairs of jobs as complements. Institutions' preferences over sets of individuals are assumed to satisfy responsiveness. However, couples' preferences over pairs of institutions are allowed to violate responsiveness. In this setting, first, we assume that institutions have a common preference over the individuals, and(i) we provide a complete characterization of all preferences of couples such that a stable matching exists under the additional assumption that couples violate responsiveness in order to be matched at the same institution, and (ii) we provide a necessary and sufficient condition on the common preference of institutions so that a stable matching exists when couples can violate responsiveness in an arbitrary manner. Finally, we relax the common preference assumption on institutions' preferences and provide a sufficient condition on the same for the existence of a stable matching