  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.
