Accommodating couples has been a longstanding issue in the design of centralized labor market clearinghouses for doctors and psychologists, because couples view pairs of jobs as complements. A stable matching may not exist when couples are present. We find conditions under which a stable matching exists with high probability in large markets. We present a mechanism that finds a stable matching with high probability, and which makes truth-telling by all participants an approximate equilibrium. We relate these theoretical results to the job market for psychologists, in which stable matchings exist for all years of the data, despite the presence of couples.
