“…Our results can be summarized as follow: For a model of trading networks with frictions (Fleiner et al, 2019) and under the assumptions of full substitutability (Sun and Yang, 2006;Ostrovsky, 2008;Hatfield et al, 2013) and the laws of aggregate demand and supply (Hatfield and Kominers, 2012;Hatfield et al, 2021), we show that -the set of competitive equilibria is a sublattice of the price space (first part of Theorem 1), -a generalized "rural hospitals theorem" holds: the difference between the number of signed downstream and the number of signed upstream contracts is the same for each firm in each equilibrium (second part of Theorem 1), -assuming additionally "bounded willingness to pay" (Fleiner et al, 2019), 2 there is an equilibrium that is most preferred by terminal sellers and an equilibrium that is most preferred by terminal buyers (Theorem 2), -a mechanism that selects buyer-optimal equilibria is group-strategy-proof for terminal buyers on the domain of unit-demand utility functions and similarly a mechanism that selects seller-optimal equilibria is group-strategy-proof for terminal sellers on the domain of unit-supply utility functions (Theorem 3).…”