Differential Game Analysis Of Supply Chain Emission Reduction Under Carbon Trading

The tendency of the global bad weather has been increasingly aggravated,and many countries have adopted a series of policies and systems for this situation.In order to restrain carbon emission,the cap-and-trade regulation,as the standard of the international carbon trading market,is playing an active role.At the same time,consumers' awareness of energy conservation and emission reduction gradually increases.Therefore,under the cap-and-trade regulation,this paper studies the differential game model of joint emission reduction strategy in the supply chain.Firstly,we consider a two-stage supply chain which has one manufacturer and one retailer.Under the cap-and-trade regulation and consumers' low-carbon preference,aiming at solving the problem of emission reduction,promotion and pricing in the low-carbon supply chain,a Stackelberg differential game model is constructed.Dynamic optimization about vertical cooperation on carbon emissions reduction is discussed in a low-carbon supply chain consisting of one manufacturer which is a leader and one retailer which is a follower.The feedback equilibrium strategy under different decision situations are obtained and compared.The long-term trajectory equation of products' carbon emissions and goodwill can be found,and the optimal value function of profit present value can be obtained respectively under different decision situations.Furthermore,the sensitivity analysis of related parameters is conducted by using the numerical simulation method.The results show that cost-sharing contract under certain conditions can achieve Pareto improvement of profits of supply chain members and the whole supply chain system.Under the three decisions,the carbon emission of the product and the optimal manufacturer's emission reduction effort decrease monotonically with time,and the goodwill increases monotonically with time,In addition,the carbon emission,the optimal manufacturer's emission reduction effort and goodwill of the product can reach a stable value as time approaches infinity.Under certain conditions,cost-sharing contracts can improve the level of the optimal retailer's promotion effort and product goodwill,but will not affect the retail price,the optimal manufacturer's emission reduction effort and carbon emissions.The optimal manufacturer's emission reduction effort under centralized decision-making scenario is first lower than those under two decentralized decision-making scenarios and then catches up at some point.Secondly,we consider a two-stage supply chain which has one manufacturer and two competing retailers.Under the cap-and-trade regulation and consumers' low-carbon preference,we present a Stackelberg differential game model that involves one dominant manufacturer and two competing retailers as the follower in the supply chain.The dynamic optimization of joint emission reduction strategy is studied in the supply chain.At the same time,the problem of supply chain coordination is studied by designing transfer payment contract.We find that the products' carbon emission and the optimal manufacturer's emission reduction effort decrease monotonically with time under certain condition,and the reduction in unit time also shows a decreasing trend.In addition,the carbon emission and the optimal manufacturer's emission reduction effort can reach a stable value as time approaches infinity under the three decisions.Under decentralized decision-making scenario,two retailers' promotion efforts will be strengthened with the increase of the competition coefficient of the two retailers' low-carbon promotion.Under centralized decision-making scenario,with the increase of the competition coefficient of the two retailers' low-carbon promotion,the two retailers' promotion efforts show the opposite trend.In addition,transfer payment contract can effectively realize supply chain coordination.