Contract design and stability in many-to-many matching

We develop a model of many-to-many matching with contracts that subsumes as special cases many-to-many matching markets and buyer–seller markets with heterogeneous and indivisible goods. In our setting, substitutable preferences are sufficient to guarantee the existence of stable outcomes; moreover, in contrast to results for the setting of many-to-one matching with contracts, if any agent's preferences are not substitutable, then the existence of a stable outcome can not be guaranteed.