Complexity dynamics analysis of a dual-channel green supply chain with government intervention and cap-and-trade regulation

Abstract This paper studies a dual-channel green supply chain consisting of one manufacturer and one retailer in presence of government green subsidy and cap-and-trade regulation policies. We first develop and analyze a single-period Stackelberg and a multi-period dynamic Stackelberg game models respectively with consistent pricing strategy. Subsequently, we extend these two game models by utilizing an inconsistent pricing strategy. The optimal solutions for the single-period Stackelberg game models in both scenarios are derived by means of the backward induction approach. Moreover, the existence and local asymptotic stability of the equilibrium points of the multi-period dynamic Stackelberg game models are examined, and the complex dynamics of chain members’ long-term strategy evolution are investigated through chaos theory and numerical simulation. Additionally, the variable feedback control and time-delay feedback control method are utilized to eliminate system chaos respectively. The results indicate that (i) The excessive fast adjustment speeds by the manufacturer have a destabilizing effect on the stability of the Nash equilibrium point. (ii) The manufacturer’s profits are improved with green subsidy degree increases, while its impact on the retailer’s profits depends on certain parameter conditions, and the high carbon trading price is disadvantage to both chain members. (iii) The system’s motion can transition from a steady state to a chaotic period through period-doubling or Neimark–Sacker bifurcations. (iv) The system’s steady state is conducive to the manufacturer, while the retailer can benefit from the system’s periodic cycles. Furthermore, both chain members’ profits are declined when the system becomes chaotic. Lastly, the variable feedback and time-delay feedback control method can effectively eliminate system chaos.