Ma, Junhai; Guo, Yuehong Research on third-party collecting game model with competition in closed-loop supply chain based on complex systems theory. (English) Zbl 1406.91025 Abstr. Appl. Anal. 2014, Article ID 750179, 22 p. (2014). Summary: 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. 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