We show that in general trading networks with bilateral contracts, a suitably adapted chain stability concept (Ostrovsky, 2008) is equivalent to stability (Hatfield and Kominers, 2012; Hatfield et al., 2013) if all agents' preferences are fully substitutable and satisfy the Laws of Aggregate Supply...

This paper presents a theory of matching in vertical networks, generalizing the theory of matching in two-sided markets introduced by Gale and Shapley. Under natural restrictions, stable networks are guaranteed to exist. The set of stable networks is a lattice, with side-optimal stable networks...

In a general model of trading networks with bilateral contracts, we propose a suitably adapted chain stability concept that plays the same role as pairwise stability in two-sided settings. We show that chain stability is equivalent to stability if all agents' preferences are jointly fully...