The Nash Equilibrium of two price competing integrated supply chains

In the literature, substantial researches have been carried out on supply chain coordination. The majority of these studies suggest a mechanism that enforces the supply chain members to follow strategies that produce the equilibrium of an integrated supply chain. Moreover, most of researches do not consider the competition among supply chains. In this study, we consider an industry including two distinct integrated supply chains which compete with each other over price. It is assumed that demand is stochastic with additive form whose random component has a uniform distribution. An algorithm is presented to calculate the Nash Equilibrium quantities of price and production amount in each chain. Furthermore, the effect of competition and demand uncertainty on the profit of the supply chains and industry are discussed in a numerical example.