We introduce a model in which firms trade goods via bilateral contracts which specify a buyer, a seller, and the terms of the exchange. This setting subsumes (manyto-many) matching with contracts, as well as supply chain matching. When firms’ relationships do not exhibit a supply chain structure, stable allocations need not exist. By contrast, in the presence of supply chain structure, a natural substitutability condition characterizes the maximal domain of firm preferences for which stable allocations always exist. Furthermore, the classical lattice structure, rural hospitals theorem, and one-sided strategy-proofness results all generalize to this setting.

We introduce a model in which firms trade goods via bilateral contracts which specify a buyer, a seller, and the terms of the exchange. This setting subsumes (manyto-many) matching with contracts, as well as supply chain matching. When firms’ relationships do not exhibit a supply chain structure, stable allocations need not exist. By contrast, in the presence of supply chain structure, a natural substitutability condition characterizes the maximal domain of firm preferences for which stable allocations always exist. Furthermore, the classical lattice structure, rural hospitals theorem, and one-sided strategy-proofness results all generalize to this setting. JEL Classification: C78, D4, L14

This note surveys recent work in generalized matching theory, focusing on trading networks with transferable utility. In trading networks with a finite set of contractual opportunities, the substitutability of agents ’ preferences is essential for the guaranteed existence of stable outcomes and the correspondence of stable outcomes with competitive equilibria. Closely analogous results hold when venture participation is continuously adjustable, but under a concavity condition on agents’ preferences which allows for some types of complementarity.

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We introduce a model in which agents in a network can trade via bilateral contracts. We find that when continuous transfers are allowed and utilities are quasilinear, the full substitutability of preferences is sufficient to guarantee the existence of stable outcomes for any underlying network structure. Furthermore, the set of stable outcomes is essentially equivalent to the set of competitive equilibria, and all stable outcomes are in the core and are efficient. In contrast, for any domain of preferences strictly larger than that of full substitutability, the existence of stable outcomes and competitive equilibria cannot be guaranteed.

We introduce a matching model in which agents engage in joint ventures via multilateral contracts. This approach allows us to consider production complementarities previously outside the scope of matching theory. We show analogues of the first and second welfare theorems, and, when agents ’ utilities are concave in venture participation, show that competitive equilibria exist, correspond to stable outcomes, and yield core outcomes. Competitive equilibria exist in our setting even when externalities are present.