The Radical Complexity of Rewiring Supplier–Buyer Networks

Colon, C. ORCID: https://orcid.org/0000-0002-4132-4648 & Bouchaud, J.-P. (2022). The Radical Complexity of Rewiring Supplier–Buyer Networks. SSRN Electronic Journal 10.2139/ssrn.4300311. (Submitted)

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Abstract

This paper questions the dynamic stability of supplier-buyer networks. We investigate a simple rewiring process, by which firms change suppliers if it increases profit, within an otherwise classical production network model with market clearing, profit-maximization, and complete information. We find that these systems exhibit extremely vast sets of path-dependent and locally-stable configurations, in which firms have no interest to change suppliers. Following an external shock, the network undergoes a cascade of rewirings and reaches a new stable configuration. However the duration of those cascades quickly increases with network size, suggesting that, in real network made of millions of firm, locally-stable configurations are not likely to be ever reached. Moreover, as soon as firms have limited visibility over their supply chain, networks fail to stabilize and keep changing configurations forever. They either drift in the topological space or alternate within a reduced set of configurations. Our results are consistent with the well-known combinatorial problems marked by rugged dynamical landscapes. Because of such a radical complexity, one cannot assume that supplier-buyer networks are in equilibrium.

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