With the growth of the world’s industrial economy, carbon dioxide emissions have snowballed, and a series of ensuing issues have endangered the sustainable development of humans and posed a threat to the health of human beings [1]. A growing number of countries believe that developing a low-carbon economy can alleviate global warming, improve the ecological environment, and promote coordinated social development. Sustainable development of the supply chain has received growing attention in a low-carbon economy. Charles, head of the UNEP, highlighted that in the next decade, sustainable supply chains will become the only supply chain model in the world (China–EU high-level forum on sustainable supply chains, 2016). Accordingly, countries have started formulating relevant low-carbon policies and measures. In 2017, the Chinese government formulated guidelines on promoting innovation and application of supply chains, as well as encouraged enterprises to engage in low-carbon manufacturing and green and sustainable management. In 2021, the South Korean government emphasized expanding cooperation with public companies in low-carbon projects, and it is expected to invest 94 trillion won in the sector by 2025. The EU introduced a plan called “Carbon Border Adjustment Mechanism” in the same year; this plan requires that all products imported into the EU must bear the cost of carbon emissions. It aims to promote the management of carbon emission reduction in the supply chain and avoid carbon leakage. In building a low-carbon city and advocating green development, Chile has fully respected the law of sustainable development and established an emission reduction office as a public institution to provide management functions, quantify carbon emission monitoring, and formulate plans to decrease carbon emissions.

The triple bottom line (TBL), first proposed by Elkington [2], believes that it is more conducive to the sustainable development of enterprises only by always adhering to the unity of corporate profitability, social responsibility, and environmental responsibility. Thus, the sustainable development of supply chains is based on the TBL, which requires strategic integration and system optimization of economic, social, and environmental objectives, involves multiple stakeholders, and requires the joint participation of supply chain members, governments, and consumers ^[3][4][3,4]. Facing the new trend of modern enterprise development and the new characteristics of market demand, problems related to low-carbon sustainable supply chain management (SSCM) have gradually developed around government regulation, supply chain member operation, and consumer purchase behavior. Meanwhile, scholars have started exploring from the standpoints of low carbon, sustainable development, and green development ^[5][6][7][5,6,7], and making suggestions for the promotion of a low-carbon economy and sustainable development of supply chains. In the context of low carbon, since the production and sales process of products is realized through the supply chain, to reduce the carbon emissions of products, different members of the supply chain play different roles; not only manufacturers need to invest in low-carbon R&D, but also retailers need to guide consumers’ low-carbon purchasing behavior through marketing means (electronic advertising, shelf display, and promotional activities). In addition, in a global Accenture survey, >80% of respondents showed a high degree of green preference when making purchase choices, suggesting that more enterprises will expand the green and low-carbon commodity market and reinforce the low-carbon and sustainable management of the supply chain. However, in the early stage of policy implementation and manufacturing and promotion of low-carbon products, enterprises often face adverse conditions, such as constraints on R&D and technological innovation funds and lack of innovation resources. Therefore, the regulatory role of the government must be brought into play, as government subsidies are indispensable [8]. Various forms of government input subsidies can accelerate the transformation and upgrading of enterprises [9], promote enterprises to conduct R&D and innovation activities, enhance the efficiency of resource use, and improve the greenness of products [10]. Exploring the investment of sustainable low-carbon products under centralized and decentralized supply chains, Dong et al. [11] reported that the government’s sustainable innovation fund stimulated the increase of orders while decreasing carbon emissions.

In recent years, many studies have investigated government subsidies and corporate carbon emission reduction and promotion. The government can play a role in macro-control. Some studies focused on the performance of government subsidies and carbon emissions. Resnier et al. ^[12][16], Toshimitsu et al. ^[13][17], and Hong et al. ^[14][18] explored the impact of government subsidies on the development of low-carbon industries. The research shows that government subsidies can not only promote the development and development of clean energy, but also promote the production and marketing of low-carbon products. Furthermore, Sheu et al. ^[15][19] found through research that government subsidies can improve the income of low-carbon enterprises. Jiang et al. ^[16][20] reported that government carbon subsidies could promote the profits of supply chain members and reduce carbon emissions. Xia and Xu ^[17][21] demonstrated that government subsidies are conducive to decreasing the impact of supply chains on the environment and improving the overall benefits of low-carbon supply chains. Li et al. ^[18][12] considered supply chain emission reduction cooperation and explored the optimal manufacturer under different government subsidies, emission reduction investment, and the government’s optimal subsidy rate. While some studies are based on different government subsidy strategies, Hafezalkotob et al. ^[19][22] compared the role of government subsidy policies and carbon tax policies, revealing that appropriate government policies can inspire manufacturers to implement low-cost policies. Carbon production reduces the carbon emissions of enterprises and promotes the low-carbon sustainable development of enterprises. Sinayi and Rasti-Barzoki ^[20][23] considered the manufacturer’s own carbon emission reduction efforts and examined the impact on the profits of the supply chain and social welfare without government subsidies and subsidies based on emission reduction levels, emphasizing that subsidies based on carbon emission reduction levels exert a positive effect on social welfare and social development. 

Meanwhile, in the study of carbon emission reduction efforts and promotion efforts of supply chain members, research has demonstrated that enterprises’ carbon emission reduction and advertising marketing of supply chain members can increase supply chain profits ^[21][24]. Green marketing of supply chain members can increase market demand ^[22][25] and enhance supply chain performance ^[23][15]. Many studies focused on the coordinated design of a cooperative emission reduction supply chain ^[24][25][26][26,27,28], and some studies examined the cooperation of manufacturers to guide retailers’ low-carbon publicity ^[27][28][29][14,29,30]. Wang et al. ^[24][26] explored the problem of carbon emission reduction when retailers are dominant within the power balance, and reported that cost sharing and wholesale price premium contracts can attain the objective of reducing total carbon emissions. Huang et al. ^[25][27] proposed cooperative emission reduction, cooperative promotion, and that there are three cooperative modes of mutual cost-sharing, as well as that mutual cost-sharing is beneficial to manufacturers’ emission reduction and retailers’ efforts to promote sales. Zu et al. ^[26][28] established a differential game model between manufacturers and their upstream suppliers, and studied the best outcomes of the two parties with different game positions. They optimized emission reduction strategies and profit levels, and further pointed out that the cooperation between the two parties can effectively reduce the carbon emissions of products and increase the profits of the supply chain. Xie et al. ^[28][29] studied the supply chain system composed of upstream manufacturers and downstream two competing retailers, indicating that all subjects of the supply chain vigorously publicize low-carbon products, to expand sales to make up for the capital investment in emission reduction. Wang et al. ^[27][14] considered that the retailer bears part of the cost of emission reduction efforts of the manufacturer, and used the differential game theory to give the optimal emission reduction effort level and publicity effort level of the manufacturer and the retailer. Zhou et al. ^[29][30] studied how to optimize the management decision-making of the low-carbon supply chain, and analyzed the impact of a cooperative publicity contract, with cooperative publicity and emission reduction cost sharing a contract on the optimal decision-making and coordination of low-carbon supply chain.