2012b): “Matching in Networks with Bilateral Contracts

We introduce a model in which firms trade goods via bilateral con-tracts 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 con-dition characterizes the maximal domain of firm preferences for which stable allocations always exist. Furthermore, the classical lattice struc-ture, rural hospitals theorem, and one-sided strategy-proofness results all generalize to this setting. The theoretical literature on two-sided matching began with the simple one-to-one (marriage) model of Gale and Shapley (1962), in which agents on opposite sides of a market (men and women) seek to match into pairs. The central solution concept in this literature is stability, the requirement that, if two agents are not matched to each other, at least one of them prefers his or her assigned partner to the other agent. Gale and Shaple