Abstract: When a brand owner selects original entrusted manufacturers (OEMs) to make products, it often selects a number of different manufacturers to produce the same type but different models of products, and determines the advertising strategies according to the corresponding market performance of different types of products. In the context of current global warming, brand owners with social responsibility cooperate with their OEMs to jointly implement their emission-reduction strategies by sharing part of the cost of carbon reduction of the OEMs. Different carbon reduction and advertising strategies will affect the profitability of OEMs by influencing the demand. Therefore, they need to study how to determine the optimal carbon reduction strategies to maximize their profit. Similarly, how to determine the optimal advertising investment and carbon reduction cooperation strategies will be core issues for brand owners. At the same time, it should be noted that consumers are not only affected by the level of carbon reduction effort when purchasing products, but also affected by reference low-carbon efforts effect formed during the past purchasing experience. That is the reference carbon reduction effect. Therefore, it is necessary to figure out the impact of reference carbon reduction effect on strategies of carbon reduction and advertising.
Considering the competition of OEMs and reference low-carbon efforts effect, a supply chain is constructed that includes two competing emission reduction OEMs and a brand owner. Issues of the dynamic strategies of the joint emissions reduction and advertising as well as supply chain coordination are analyzed based on the differential game theory. The strategies of supply chain in decentralized and centralized decision-making models have been analyzed. The differences the level of emission reduction efforts, the advertising level and the present value of the total profit between the two decision-making models have been compared. It is found that when the marginal revenue of manufacturers is low in the cooperative decision-making case, the level of carbon reduction effort is higher than that in the decentralized decision-making case; otherwise, the level of carbon reduction is higher in the decentralized decision-making case. The level of advertising in the centralized and decentralized decision-making cases does not depend on the marginal revenue of the brand owner, but depends on the relative marginal revenue of OEMs. The effects of the memory and reference parameters are investigated with the numerical analysis. To obtain the supply chain profit of the centralized decision-making case in the decentralized case, a two-way cost sharing contract is designed that OEMs and the brand owners share the carbon-reduction and advertising costs from each other. The profits of the brand owner and OEMs in the decentralized decision-making and two-way cost sharing contract cases are compared with numerical analysis. It is found that the two-way cost sharing contract does not present the Pareto improvement for supply chain members. To settle this issue, the transfer payment contract is offered to achieve the self-execution of the contract.

Key words: reference low-carbon efforts effect, low-carbon supply chain coordination, cost sharing contract, differential game