Coordination contracts and numerical analysis of low-carbon competitive supply chains under the influence of low-carbon goodwill

Introduction: Under the dual opportunities of low-carbon consumption preference and online consumption platforms, vendors' low-carbon advertising incursions provide opportunities for decarbonization and market position enhancement, as well as further research on the value of low-carbon advertising. This study aims to explore the contractual choices of green vendors' online channels participating in low-carbon advertising competition under the low-carbon goodwill effect, and to simulate and evaluate the contractual choices of supply chain members.Methods: Using differential games, through the innovative application of the traditional low-carbon goodwill model and the introduction of the low-carbon advertising competition intensity coefficient, we design one-way and two-way cost-sharing contracts under low-carbon competition, coordinate the vicious competition in the supply chain, and provide contractual choices for supply chain participants.Results and discussion: Under the low-carbon advertising competition decision, the manufacturer has an absolute low-carbon market advantage, but the interests of all supply chain members are weakened, and interestingly, the manufacturer, who dominates the market, is the facilitator of the contractual agreement. Second, well-designed pacts can provide manufacturers and traders with more options for low-carbon strategies. Although both one-way and two-way cost-sharing pacts can generate Pareto gains for the supply chain and its members in advertising competition, two-way cost-sharing pacts are superior to one-way pacts in terms of coordination advantages. In addition, an important finding is that greater profit growth can be achieved through contractual cooperation in low-intensity advertising competition. Thus, moderate competition is desirable, while excessive competition can harm the supply chain system. Manufacturers should actively urge retailers to cooperate in order to optimize profits and establish long-term stable partnerships between upstream and downstream firms in green supply chains.