'Stability in Supply Chain Networks:' An Alternative Approach

We introduce a version of the Cumulative Offer Algorithm of Hatfield and Milgrom (2005) modified for the supply chain networks setting of Ostrovsky (2008). The algorithm provides an alternative proof for existence of a chain stable network. When sellers propose downstream, the algorithm produces the allocation that is optimal for suppliers of basic inputs. Moreover, the proof illustrates the importance of Aygun and Sonmez (2012b)'s Irrelevance of Rejected Contracts (IRC) condition for establishing existence in the supply chain networks setting.