On the Efficiency of Stable Matchings in Large Markets

Stability is often the goal for clearinghouses in matching markets, such as those matching residents to hospitals, students to schools, etc. Stable outcomes absent transfers need not be utilitarian efficient, suggesting the potential value of trans-fers. We study the wedge between stability and efficiency in large one-to-one matching markets. We show stable matchings are efficient asymptotically for a large class of preferences. In these environments, stability remains an appealing objective even on efficiency grounds, and monetary transfers are not necessary for efficiency purposes. Nonetheless, for severely imbalanced markets, when preferences entail sufficient idiosyncrasies, stable outcomes may be inefficient even asymptotically