Stable Production Networks

One of the key features which promote growth of industrial clusters is collaboration among firms within such clusters. Collaboration among firms leads to the formation of networks. Stability of these networks is vital to the sustainability of the particular firms. In this paper, we model a supply chain network where a set of downstream firms (players) source inputs from upstream firms (players) who manufacture goods, add value to the products and resell them. The upstream firms produce identical goods and compete on quantities to sell these goods to the downstream firms. The upstream firms procure goods from the downstream firms and sell them. Additionally, upstream firms network among themselves so as to reduce their costs. We model this setting as a two-stage n-player strategic network formation game. Firms decide their links before competing on quantities in the second stage of the game. Using the defined model, we derive equilibrium quantities and profits as a function of the network structure and number of firms. Following which we analyze the conditions under which different stable network emerge. Our analysis brings forth several interesting insights such as higher connections among downstream players lead to increased profits for upstream manufacturers. From the network stability perspective, we obtain the conditions under which regular, star, etc. network structures are pairwise and bilaterally stable. Furthermore, we also find the conditions under which core–periphery network structures emerge and are stable.