Hatfield and Kominers (2012) introduced a model of matching in networks with bilateral contracts and showed that stable outcomes exist in supply chains when firms' preferences over contracts are fully substitutable. Hatfield and Kominers (2012) also asserted that in their setting, full substitutability is equivalent to the assumption that all indirect utility representations of each firm's preferences are quasisubmodular; we show here that this claimed equivalence result does not hold in general. We show instead that full substitutability is equivalent to weak quasisubmodularity of all indirect utility representations.
Hatfield, John William, Ravi Jagadeesan, and Scott Duke Kominers.
"Matching in Networks with Bilateral Contracts: Corrigendum."
American Economic Journal: Microeconomics,
Bargaining Theory; Matching Theory
Network Formation and Analysis: Theory