We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and...

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 study a simple model of a decentralized market game in which firms make directed offers to workers. We focus on markets in which agents have aligned preferences. When agents have complete information or when there are no frictions in the economy, there exists an equilibrium that yields the...