Research on Third-Party Collecting Game Model with Competition in Closed-Loop Supply Chain Based on Complex Systems Theory

This paper studied system dynamics characteristics of closed-loop supply chain using repeated game theory and complex system theory. It established decentralized decision-making game model and centralized decision-making game model and then established and analyzed the corresponding continuity system. Drew the region local stability of Nash equilibrium and Stackelberg equilibrium, and a series of chaotic system characteristics, have an detail analysis of the Lyapunov index which is under the condition of different parameter combination. According to the limited rational expectations theory, it established repeated game model based on collection price and marginal profits. Further, this paper analyzed the influence of the parameters by numerical simulations and concluded three conclusions. First, when the collection price is to a critical value, the system will be into chaos state. Second, when the sale price of remanufacturing products is more than a critical value, the system will be in chaos state. Last, the initial value of the collection price is sensitive, small changes may cause fluctuations of market price. These conclusions guide enterprises in making the best decisions in each phase to achieve maximize profits.