In the context of reducing carbon emissions in the automotive supply chain, collaboration between vehicle manufacturers and retailers has proven to be an effective measure for enhancing carbon emission reduction within the enterprise. This study aims to evaluate the effectiveness of such collaboration by constructing a differential game model that incorporates carbon trading and consumer preferences for low-carbon products. The model examines the decision-making process of an automotive supply chain comprising a vehicle manufacturer and multiple retailers. By utilizing the Hamilton-Jacobi-Bellman equation, we analyze the equilibrium strategies of the participants under both a decentralized model and a Stackelberg leader-follower game model. In the decentralized model, the vehicle manufacturer optimizes its carbon emission reduction efforts, while each retailer independently determines its low-carbon promotion efforts and vehicle retail price. In the Stackelberg leader-follower game model, the vehicle manufacturer cooperates with the retailers by offering them a subsidy. Consequently, the manufacturer plays as the leader, making decisions on carbon emission reduction efforts and the subsidy rate, while the retailers, as followers, compute their promotion efforts and retail prices accordingly. Through theoretical analysis and numerical experiments considering the manufacturer's and retailers' efforts, the low-carbon reputation of vehicles, and the overall system profits under both models, we conclude that compared to the decentralized model, where each party pursues individual profits, the collaboration in the Stackelberg game yields greater benefits for both parties. Furthermore, this collaborative approach promotes the long-term development of the automotive supply chain.

翻译：在汽车供应链碳减排的背景下，整车制造商与零售商之间的合作已被证明是提升企业碳减排效果的有效措施。本研究旨在通过构建纳入碳交易与消费者低碳产品偏好的微分博弈模型，评估此类合作的有效性。该模型考察了由一家整车制造商与多家零售商构成的汽车供应链决策过程。我们利用汉密尔顿-雅可比-贝尔曼方程，分析了分散模型与Stackelberg主从博弈模型下参与者的均衡策略。在分散模型中，整车制造商优化其碳减排努力，而各零售商独立确定其低碳促销努力及车辆零售价格。在Stackelberg主从博弈模型中，整车制造商通过向零售商提供补贴实现合作。由此，制造商作为领导者，决策碳减排努力与补贴率，而零售商作为跟随者，据此计算其促销努力与零售价格。通过理论分析及数值实验，综合考量两种模型下制造商与零售商的努力程度、车辆低碳声誉及系统总利润，我们得出结论：相较于各方追求个体利润的分散模型，Stackelberg博弈下的合作为双方带来更大收益。此外，这种合作方式有助于促进汽车供应链的长期发展。