Dynamic decision-making and coordination of low-carbon closed-loop supply chain considering different power structures and government double subsidy

Low-carbon closed-loop supply chain (LC-CLSC) plays an important role in realizing a low-carbon circular economy. In order to facilitate governments to make emission reduction subsidy and recycling subsidy decisions and LC-CLSC members to formulate pricing, emission reduction investment and recycling investment decisions, this paper proposes multiple three-level differential game models of a LC-CLSC involving the manufacturer, retailer and government considering the dynamic characteristics of product goodwill and recycling rate. Under the four scenarios of three different power structures: manufacturer-led, retailer-led and non-led, and centralized decision-making, some critical equilibrium results are first solved and discussed, including government’s optimal emission reduction subsidy and recycling subsidy rates, the manufacturer’s wholesale price and emission reduction investment, the retailer’s retail price and recycling investment, product goodwill and waste product recycling rate, profits of the manufacturer, retailer and government, etc. To further achieve the LC-CLSC coordination, the contracts under three different power structures are designed, and the conditions that the coordination parameters satisfy are given. Through mathematical derivation of equilibrium results and sensitivity analysis with the help of numerical examples, this paper finds that the government subsidy rates are dependent on the power status between manufacturers and retailers, and the weaker party will get higher subsidy rate. The government subsidy mechanism can significantly reduce the gaps between the manufacturer-led and retailer-led cases, such as manufacturer’s emission reduction investment, the retailer’s recycling investment, steady-state retail price, and product goodwill and recycling rate. Under the effect of the government subsidy mechanism, the non-led case is more conducive to the recycling of waste products and the improvement of social welfare than the unilateral domination cases. The findings can help manufacturers and retailers in the LC-CLSC formulate optimal strategies like pricing, emission reduction and recycling, and develop coordination contracts to further improve the overall performance of the supply chain according to their different power structures. More importantly, they can also help governments make optimal emission reduction and recycling subsidy decisions according to member companies’ different power structures so as to improve subsidy efficiency.Graphical abstract