Dynamic game study of multi-channel supply chain under cap-and-trade regulation

This work focuses on the dynamic complexity study of a multi-channel supply chain composed of a manufacturer, an e-retailer, and a traditional retailer under cap-and-trade regulation. A long-term dynamic Stackelberg game model is studied in three situations: without cap-and-trade regulation, grandfathering approach, and benchmarking approach. This model is further discussed by means of the stable region diagram, 2D and 3D bifurcation diagrams, and the largest Lyapunov exponent diagram. The profit, carbon emission, and social welfare of the supply chains under the three different situations are compared. The results suggest that adjustments to order quantity, consumers' channel preference, and low-carbon preference should be kept within a suitable range. The benchmarking approach is more effective than the grandfathering approach in encouraging manufacturers to pay more attention to low-carbon products. From a societal point of view, the benchmarking approach can help the whole supply chain obtain more total profit and more total social welfare, and it can lower total carbon emissions. The parameter control method is further used to control the chaos in the system.