Stable supply chains

Abstract

We generalize stability to supply chains with circles. Similarly to stable mach- ings, a supply chain is stable is there is no blocking walk, where the �rms would like to buy or sell more, and possibly dropping some of their current contracts. We show that if the choices of the �rms satisfy some natural properties, there always exist a stable supply chain. We introduce four models: the choices of the agents can di�er if there is money in the market on not, and they can have discrete or continouos quantities of traded goods. In the case without money we lean on Tarski's �xed point theorem, in the case with money, the solution is related to the maximum weighted subsets.