Joint emission reduction dynamic optimization and coordination in the supply chain considering fairness concern and reference low-carbon effect

In the context of low-carbon economy, in order to explore the impact of the fairness concern and reference low-carbon effect on supply chain members' balanced emission reduction decisions and profits, supply chain joint emission reduction dynamic optimization models under four different scenarios are built, in which the manufacturer's optimal emission reduction strategy, the retailer's optimal low-carbon promotion strategy and other equilibrium solutions are solved by differential game theory. On the basis of analysis, a contract is designed to achieve the coordination of the supply chain when members are fairness concern. Some findings are as follows. First, when consumers' purchasing behavior is significantly affected by the reference low-carbon effect, and they have higher expectations for the product's emission reduction level, consumers' reference low-carbon effect will discourage the manufacturer's enthusiasm to reduce emissions, and do harm to the profits of the manufacturer and the retailer. Second, the fairness concern behavior of both parties will aggravate the adverse effects of reference low-carbon effect, bring a detrimental effect on the performance of the supply chain, aggravate the double marginal effect of the supply chain, and cause continuous negative social influence. Third, the bilateral cost-sharing contract can encourage the manufacturer to increase emission reduction investment, the retailer to increase low-carbon promotion investment, and can achieve a Pareto improvement of both parties' profits and utilities. In addition, the two cost-sharing ratios are only proportional to the marginal revenue and fairness concern intensity of both parties. Finally, when the two cost-sharing ratios and the revenue-sharing coefficient meet a certain relationship and are within a reasonable range, the bilateral cost sharing-revenue sharing hybrid contract can reduce the double marginal effect and achieve supply chain coordination.