Abstract: Manufacturer (remanufacturer) and a retailer (collector)dynamic equilibrium strategies in a closed-loop supply chain system are studied, which consists on a leader, manufacturer (remanufacturer), and a follower, retailer (collector) with "jealousy/pride" fairness-concern behavior.First,the random evolution process of the recovery rate of waste products in closed-loop supply chain system is described by using the ITO process, its expected profit functional is given by manufacturer's profit structure, andits expected utility functional is constructed based on retailer's "jealousy/pride" model.Therefore, the stochastic differential game model of closed-loop supply chain system is established.By using stochastic differential game theory, the partial differential equations which the optimal value function of the manufacturer and retailer should be satisfied are given. By solving the partial differential equations, the optimal value function of manufacturer and retailer respectively is obtained. By using optimal value functionofmanufacturer and retailer, manufacturer's wholesale price dynamic equilibrium strategy is obtained,the retailer's selling price and recycling investment dynamic equilibrium strategy. In order to grasp the statistical characteristics of the evolution process of waste products, the stochastic evolution nature of recovery of waste products is revealed. By numerical example, impact of retailer's degree of fairness on agents'equilibrium strategies and performance arestudied.The results show that the higher the retailer's degree of fairness, the lower the manufacturer's equilibrium wholesale price and its optimal value. Unlike the manufacturer, the retailer's degree of fairness will increase its optimal value function. In addition, the higher theretailer'sdegree of fairness, the lower the collecting rate of the system is.

Key words: Closed-loop supply chain, stochastic differential game, fairness behavior, retailercollect