Abstract: A three-level supply chain consisting of a supplier, a manufacturer and a retailer is considered, and the manufacturer sets up a dual channel to sell low-carbon products. Taking the product emission reduction as the state variable, the manufacturer-led vertical upward and vertical downward cooperative emission reduction differential game models are constructed. This paper first studies the optimal equilibrium strategy of supply chain members under different cooperation directions, and then compares and analyzes the difference between the optimal trajectory curves of product emission reduction in vertical upward and vertical downward cooperative emission reduction modes. Finally, an example is used to analyze the model. It is found that the optimal trajectory of product emission reduction gradually increases to a stable state whether in vertical upward or downward cooperative emission reduction mode. Compared with manufacturers and suppliers, when manufacturers choose to cooperate with retailers to reduce emissions, manufacturers' efforts and profits are higher, and followers ' efforts are more motivated, but manufacturers need to bear more cost of reducing emissions. In vertical upward cooperation mode, the cost sharing ratio is positively correlated with carbon trading price, while in downward cooperation mode, the cost sharing ratio is U-shaped.

Key words: carbon cap and trade policy , dual-channel supply chain , vertical cooperation , dynamic emission reduction