Emission reduction cooperation in a dynamic supply chain with competitive retailers

The increasing carbon emissions cause severe environmental issues that threaten the survival of human beings. Such a situation promotes supply chain firms and governments to take various measures to achieve the sustainable goal. This paper investigates the cost-sharing cooperation strategy of emission reductions in a dynamic supply chain consisting of a manufacturer and two distinct retailers with different scales. In the presence of carbon tax and green reputation, we model a Stackelberg differential game to derive and compare the optimal equilibrium decisions and further conduct a numerical study to analyze the chain members' profits between the cases of no cost sharing and cost sharing. The manufacturer can actualize this sharing, respectively, with either of the competitive retailers. The results show that cost sharing is a better choice for supply chain members than no sharing. In the cost-sharing scenario, the manufacturer and two retailers prefer the case in which the emission reduction cost that a retailer undertakes is relatively high, because the manufacturer can increase emission reduction level to build its green reputation, and thereby the retailers can improve profits. When the proportion of emission reduction cost that a retailer undertakes locates in a certain interval, all the supply chain participants can be better off in the scenario where small-scale retailer shares the emission reduction cost. In addition, the increase in carbon tax improves the flexibility of cost-sharing ratio for the members achieving this consensual scenario on the cost-sharing cooperation.