Matching with Multilateral Contracts

In many matching environments, agreements are multilateral and/or have externalities. We show that stability in these environments depends on agents' aggregate choice behavior. Two different conditions on aggregate choice ensure a stable outcome exists. One applies when contracts are substitutes; the other ensures a unique stable outcome even without substitutability. Our results apply matching-theoretic techniques to environments where agents' interactions cannot be described by independent bilateral agreements, and also accommodate markets without a two-sided or supply chain structure. Our equivalent characterization of stability also makes computing stable outcomes easier, even in environments outside the scope of our existence results.