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, rst we assume that institutions have a common preference over individuals, and we provide:(i) 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) a necessary and sufficient condition on the common preference of institutions so that a stable matching exists when couples canviolate responsiveness in an arbitrary manner.Next, we weaken the common preference assumption on institutions' preferences by requiring common preference only over the members of each couple. In this setting, we provide:(i) a complete characterization of all preferences of couples such that stable matching exists, and(ii) a sufficient condition on the preferences of individuals' such that a stable matching exists