Matching in Networks with Bilateral Contracts

John William  Hatfield; Scott Duke Kominers

Article | American Economic Journal: Microeconomics

Matching in Networks with Bilateral Contracts

by John William Hatfield and Scott Duke Kominers

Abstract

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 (many-to-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 are guaranteed to exist. Furthermore, the classical lattice structure, rural hospitals theorem, and one-sided strategy-proofness results all generalize to this setting. (JEL C78, D85, D86, L14)

Keywords: Contracts; Market Design; Marketplace Matching; Supply Chain;

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Hatfield, John William, and Scott Duke Kominers. "Matching in Networks with Bilateral Contracts." American Economic Journal: Microeconomics 4, no. 1 (February 2012): 176–208.

This paper develops a class of equilibrium-independent predictions of competitive equilibrium with indivisibilities. Specifically, we prove an analogue of the “Lone Wolf Theorem” of classical matching theory, showing that when utility is perfectly transferable, any agent who does not participate in trade in one competitive equilibrium must receive her autarky payoff in every competitive equilibrium. Our results extend to approximate equilibria and to settings in which utility is only approximately transferable.

Hatfield and Kominers (2012) introduced a model of matching in networks with bilateral contracts and showed that stable outcomes exist in supply chains when firms' preferences over contracts are fully substitutable. Hatfield and Kominers (2012) also asserted that in their setting, full substitutability is equivalent to the assumption that all indirect utility representations of each firm's preferences are quasisubmodular; we show here that this claimed equivalence result does not hold in general. We show instead that full substitutability is equivalent to weak quasisubmodularity of all indirect utility representations.

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Matching in Networks with Bilateral Contracts

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