Research on low-carbon closed-loop supply chain strategy based on differential games-dynamic optimization analysis of new and remanufactured products

With the current increasing global demand for low-carbon and environmentally friendly products, promoting the sustainability of closed-loop supply chains has become one of the key measures. However, consumers often do not regard remanufactured products as equivalent to new products. Therefore, this paper proposes a dynamic closed-loop supply chain that incorporates consumers' purchasing preferences to model a long-term game with product differentiation. Moreover, to enhance consumer acceptance of remanufactured products and reduce manufacturers' costs, low-carbon technologies and cost-sharing mechanisms are introduced. In this way, we construct a differential game in which the manufacturer sells new and remanufactured products through a retailer and makes decisions about the level of low-carbon technology in the remanufacturing process. Based on the theory of differential games, this paper analyzes three different power structures: the manufacturer-dominated Stackelberg game, the Nash game, and the retailer-dominated Stackelberg game. The optimal low-carbon technology level and pricing strategy are obtained by applying Pontryagin's maximum principle. The study shows that the retailer-led Stackelberg game helps retailers maximize profits, while the Nash game enables the entire closed-loop supply chain system to achieve the highest overall profits. This paper innovatively integrates low-carbon technologies into the dynamic game model of the remanufacturing process and reveals how the game behavior of supply chain participants affects the application of low-carbon technologies and the overall profit of the supply chain by comparing the cost-sharing mechanisms under different power structures. The results provide important theoretical support and practical references for closed-loop supply chain management with product differentiation.