Trading Networks with Bilateral Contracts
For economists studying matching in trading networks, this provides a new stability concept that guarantees existence under standard conditions, extending known results from simpler settings.
This paper addresses the non-existence of stable outcomes in trading networks with bilateral contracts by introducing trail stability, a new solution concept. It proves that trail-stable outcomes always exist under full substitutability and establishes lattice structure, rural hospitals theorem, strategy-proofness, and comparative statics.
We consider a model of matching in trading networks in which firms can enter into bilateral contracts. In trading networks, stable outcomes, which are immune to deviations of arbitrary sets of firms, may not exist. We define a new solution concept called trail stability. Trail-stable outcomes are immune to consecutive, pairwise deviations between linked firms. We show that any trading network with bilateral contracts has a trail-stable outcome whenever firms' choice functions satisfy the full substitutability condition. For trail-stable outcomes, we prove results on the lattice structure, the rural hospitals theorem, strategy-proofness, and comparative statics of firm entry and exit. We also introduce weak trail stability which is implied by trail stability under full substitutability. We describe relationships between the solution concepts.