  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.
