Abstract
We consider general networks of bilateral contracts that include supply chains. We define a new stability concept, called trail stability, and show that any network of bilateral contracts has a trail-stable outcome whenever agents' choice functions satisfy full substitutability. Trail stability is a natural extension of chain stability, but is a stronger solution concept in general contract networks. Trail-stable outcomes are not immune to deviations of arbitrary sets of firms. In fact, we show that outcomes satisfying an even more demanding stability property -- full trail stability -- always exist. For fully 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 pin down a condition under which trail-stable and fully trail-stable outcomes coincide. We then completely describe the relationships between various other concepts. When contracts specify trades and prices, we also show that competitive equilibrium exists in networked markets even in the absence of fully transferable utility. The competitive equilibrium outcome is (fully) trail-stable.
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