Abstract: Under the tremendous pressure of global climate issue, developing low-carbon economy based on low energy consumption, low emission and low pollution has gradually become a core strategy for the world to cope with climate change. The low-carbon economy mode has a great influence on supply chain's competition regulations, cost composition and ways of operation. Therefore, it is necessary to explore the theory and practice of low-carbon supply chain. Through literature review, most literature ignore the dynamic characteristics of the low-carbon level and low-carbon goodwill of the product. In addition, there is little literature of low-carbon supply chain optimization and coordination considering decision makers' Nash bargaining fairness concerned behavior. In this paper, a utility system about fairness concerns is developed based on the Nash bargaining theory, and the dynamic characteristics of low-carbon level and low-carbon goodwill are taken into consideration. The effect of each member's fairness concerns on the retailer's low-carbon advertising strategy and the manufacturer's emission reduction strategy are explored utilizing the differential games theory and method. Through the contrastive analysis, it is discovered that the low-carbon level is higher in the centralized decision-making mode. On this basis, a two-way cost-sharing contract is designed to coordinate the decentralized supply chain. Finally, based on the parameter values chosen from the previous literature (e.g. Du et al., 2015^[2]; Andre et al., 2011^[17]), the validity of the contract is verified and the sensitivity analysis of key parameters is also presented by a numerical example. It is shown that if the manufacturer's marginal profit rate in the total supply chain is low, the manufacturer will not invest in emission reduction. The manufacturer is willing to undertake part of the advertising cost if the parameters satisfy certain conditions. The manufacturer's fairness concerns have negative effect on the development of low carbon economy for the enterprises in the supply chain. Appropriate attention of the retailer to the fairness can increase revenues of its own and the whole supply chain system. Compared with the decentralized decision-making mode, the utility and the profit of each member in the supply chain under the two-way cost-sharing contract are all improved. In this study, the scope and content of the low-carbon supply chain optimization and coordination problem under the consideration of decision makers' behavior are enriched, and the guidance for the related application of the differential games is provided.

Key words: supply chain coordination, Nash bargaining, differential games, fairness concern, low-carbon goodwill