Supply chain joint emission reduction differential decisions and coordination considering altruistic behavior and reference low-carbon effect

In the context of low-carbon economy, consumers’ reference low-carbon effect and supply chain members’ altruistic behavior are becoming factors that cannot be ignored, while there is currently little literature which synthetically studies the effect of consumers’ reference low-carbon effect and supply chain members’ altruistic behavior on supply chain members’ decisions from a long-term and dynamic perspective. Therefore, we introduce consumers’ reference low-carbon effect into the product demand function and introduce the altruistic behavior of supply chain members into their decision-making objective functions for the first time and then build differential game models based on emission reduction and low-carbon goodwill under four decision scenarios. We obtain the manufacturer’s and the retailer’s optimal emission reduction strategies and other equilibrium solutions by differential game theory and confirm the conditions for the cost-sharing contract to achieve coordination. Compared with previous studies, we obtain some new findings. First, consumers’ reference low-carbon effect will harm the profits of the manufacturer and the retailer and discourage the manufacturer’s enthusiasm to reduce emissions and retailer’s enthusiasm for low-carbon publicity. Second, the altruistic behavior of the manufacturer and the retailer can not only weaken the negative impact of the reference low-carbon effect, but also promote both parties to actively reduce emissions, help achieve Pareto improvement of their own profit and utilities, and obtain additional social welfare. Third, the cost-sharing contract can encourage the manufacturer to increase emission reduction investment without affecting the retailer’s low-carbon publicity investment and can achieve a Pareto improvement of both parties’ profits and utilities. In addition, the cost-sharing ratio is only proportional to the marginal profits and altruistic intensity of both parties, and is not affected by the reference low-carbon effect. Meanwhile, the cost-sharing ratio will decrease as the manufacturer’s marginal profit and altruistic intensity increase and will increase as the retailer’s marginal profit and altruistic intensity increase. In particular, when the retailer is completely altruistic, the cost-sharing contract can achieve perfect coordination of the supply chain.