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...

In this note, I extend the work of Echenique (Amer. Econ. Rev. 102(1): 594-601, 2012) to show that under the assumption of unilaterally substitutable preferences a matching market with contracts may be embedded into a matching market with salaries. In particular, my result applies to the...