Dynamic decision-making and differential game analysis of ESG-constrained closed-loop supply chains under cap-and-trade regulation

This paper constructs a differential game model for a closed-loop supply chain operating under environmental, social, and governance (ESG) constraints within a cap-and-trade setting. The framework captures emission reduction activities, recycling investments, goodwill dynamics, and stochastic shocks, and compares decentralized and centralized decision-making under two allocation criteria: grandfathering and benchmarking. Equilibrium strategies are derived and supported by numerical simulations to trace the dynamic trajectories of abatement, recycling, goodwill, and profit, while also assessing the roles of carbon pricing, recycling revenues, and quota policies. The analysis highlights three major findings. First, the benchmarking criterion creates stronger incentives for emission reduction and recycling, with centralized governance amplifying this advantage. Second, random disturbances leave the long-term equilibrium unchanged but may cause short-term shifts in goodwill and profit rankings. Third, centralized coordination raises overall profitability yet proves less robust, whereas decentralized structures favor stability at the expense of efficiency. Together, these results contribute to the literature on closed-loop supply chains and offer practical implications for aligning economic performance, system stability, and environmental objectives.