Paths to stability for matching markets with couples

We study two-sided matching markets with couples and show that for a natural preference domain for couples, the domain of weakly responsive preferences, stable outcomes can always be reached by means of decentralized decision making. Starting from an arbitrary matching, we construct a path of matchings obtained from 'satisfying' blocking coalitions that yields a stable matching. Hence, we establish a generalization of Roth and Vande Vate's [Roth, A.E., Vande Vate, J.H., 1990. Random paths to stability in two-sided matching. Econometrica 58, 1475-1480] result on path convergence to stability for decentralized singles markets.Furthermore, we show that when stable matchings exist, but preferences are not weakly responsive, for some initial matchings there may not exist any path obtained from 'satisfying' blocking coalitions that yields a stable matching.