We develop the theory of stability for aggregate matchings used in empirical studies and establish fundamental properties of stable matchings including the result that the set of stable matchings is a non-empty, complete, and distributive lattice. Aggregate matchings are relevant as matching...

We experimentally study the Gale and Shapley (1962) mechanism, which is utilized in a wide set of applications, most prominently the National Resident Match- ing Program (NRMP). Several insights come out of our analysis. First, only 48% of our observed outcomes are stable, and among those a...