Generalized Nash Equilibrium in Two-Echelon Supply Chain Networks: Analyzing Intra-Entity Collaboration and Inter-Entity Competition

As an important research direction in the supply chain network, multi-echelon supply chain networks have attracted significant attention. However, existing studies predominantly focus on competitive relationships among entities within the same layer, neglecting the coexistence of intra-entity collaboration and inter-entity competition in real-world scenarios. In addition, the interactions between the upstream and downstream layers in a two-echelon supply chain network with multiple suppliers and producers remain to be investigated. To address these gaps, this paper introduces a novel framework that incorporates collaboration factors, utilizing internal and external coupling constraints to characterize cooperative and competitive relationships. By employing an N-coalition game to solve subgames within each layer, we model the interactions between upstream and downstream layers and propose a generalized Nash equilibrium seeking algorithm for such networks. The convergence of the proposed algorithm is strictly proved. The effectiveness of the algorithm is illustrated by the case of a petrochemical supply chain network.