Complex Dynamics of a Low-Carbon Supply Chain with Government Green Subsidies and Carbon Cap-and-Trade Policies

Abstract

This paper considers a two-echelon supply chain consisting of one government, one manufacturer and one retailer in the presence of government green subsidies and carbon cap-and-trade policies. The manufacturer adopts eco-friendly technologies to produce green products for curbing carbon emissions, and the retailer is responsible for selling green products to consumers who exhibit low-carbon preferences. Two noncooperative game models, that is, the manufacturer-led Stackelberg model and the vertical Nash model, are developed under static and dynamic settings, respectively. The static analytical solutions of the models are derived by using game theory, and their complex dynamical behaviors are explored via bifurcation and chaos theory. The results indicate that the excessively large adjustment parameters of the players will destabilize the stability of the Nash equilibrium point, leading to more complicated behaviors such as bifurcation and chaos. The higher consumers’ low-carbon preference has a destabilization effect on the system’s stability while the carbon trading price may be a stabilizing or a destabilizing factor for the system under different scenarios. Besides, the influence of the government’s green subsidy rate on the system’s stability is not obvious in most cases. Furthermore, when the system enters into periodic cycles and chaotic motions resulting from the overly fast adjustment speeds, the channel members’ performance may be elevating or declining in different models. Therefore, the chaos in the low-carbon supply system is not always detrimental to the channel members.