A cumulative offer process for supply chain networks

We introduce a version of the Cumulative Offer Algorithm of Hatfield and Milgrom (Am Econ Rev 95(4):913–935, 2005) modified for the supply chain networks setting of Ostrovsky (Am Econ Rev 98(3):897–923, 2008). The algorithm provides an alternative proof for existence of a chain stable network. Moreover, we show that when choice functions satisfy same-side substitutes and cross-side complements, and the Law of Aggregate Demand and Supply, then contracts satisfy Irrelevance of Rejected Contracts condition, a condition implicitly assumed in Ostrovsky (2008).