Abstract: Based on the dynamic environment, the selection of manufacturers' cooperation strategies in closed-loop supply chains with third parties were studied. Four cooperation strategies were established: manufacturers only cooperate with recyclers or retailers; manufacturers cooperate with recyclers and retailers; and they do not cooperate. Differential game theories were used to solve the four models to get the optimal control strategy under different cooperation strategies. Several results were conclused. 1) When manufacturers, retailers and recyclers all cooperate, consumer welfare is the highest of the four models. 2) When manufacturers, retailers and recyclers do not cooperate, the retail price of the product is the highest among the four modes. 3) When manufacturers, retailers, and recyclers all cooperate, recycling efforts are the greatest. When manufacturers, retailers, and recyclers do not cooperate, recycling efforts are minimal, when manufacturers and retailers cooperate and when manufacturers work with recyclers, the size of the recycling effort is related to the payment price paid by the manufacturer to the recycler. 4) There is a possibility of cooperation between the manufacturer and the retailer or recycler. 5) When manufacturers, retailers, and recyclers work together, the total profits of the supply chain are the greatest, and the total profits of the supply chain are the smallest when manufacturers, retailers, and recyclers have no cooperation. The total profit of the supply chain is related to the transfer payment, the recovery cost coefficient and the unit cost of remanufacturing savings.

Key words: closed-loop supply chain, remanufacturing, cooperation strategy, differential games, open-loop control strategy