Abstract: Considering two closed-loop supply chains consisting of one manufacturer and one retailer respectively, where the retailers recover used products, three models such as EPEC (Equilibrium Problems with Equilibrium Constrains) model, Nash equilibrium model and MPEC (Mathematical Programs with Equilibrium Constrains) model are set up together with their solving processes by using the game theory and equilibrium analysis method, which respectively correspond to three situations that two closed-loop SCs are decentralized SCs or centralized SCs or one decentralized SC and one centralized SC. The comparison of three models shows that the centralized control mode is a dominative strategy under SC competition. Then a wholesale price plus recovery subsidy contract is put forward to coordinate decentralized SC obtaining centralized SC under SC competition. Finally, a numerical example and sensitive analysis is performed, which shows the rationality of models, the validity of the contract mentioned above and the affection of related parameters.

Key words: closed-loop supply chain, supply chain competition, supply chain coordination, game theory, equilibrium analysis method