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Carbon emission reduction (CER) in the construction industry can aid in achieving the international community's carbon neutrality target. However, the low motivation of construction enterprises to reduce carbon emissions and the unsatisfactory effect of CER are still unresolved issues. This study aims to address these issues by constructing a building supply chain (BSC) consisting of a developer and a contractor using government subsidies and cost-sharing contracts. The optimal government subsidy and feedback equilibrium strategies of the BSC are examined using a combination of differential game theory and numerical simulations. The findings demonstrate that (1) cost-sharing contracts may enhance developer and contractor profits and building CER, goodwill, and demand without relying on government subsidies; (2) when subsidized by the government, each equilibrium strategy meets or exceeds the performance of the centralized model, with the cost-sharing contract having a negligible effect on the enhancement of each equilibrium strategy; and (3) both the game structure and the positioning of construction enterprises in the BSC are connected to the number of government subsidies. The city of Shenzhen, one of China's first low-carbon pilot cities, provides a realistic environment for the simulation analysis, with the Block K residential building in Nanshan District serving as a case study. Furthermore, this work contributes to the body of knowledge by proposing a novel CER model for the BSC using differential game theory. The research provides new insights into the role of government subsidies in shaping profit distribution, game structure, and enterprise positioning. Findings demonstrate the value of cost-sharing contracts in improving CER, goodwill, demand, and profits when implemented collaboratively. This advances the theoretical understanding of incentives and strategies for promoting CER in construction. This research highlights the importance of collaborative efforts between the government and the building supply chain (BSC) to promote sustainable construction and carbon emission reduction (CER). The study found that government subsidies can be an effective tool to encourage developers and contractors to adopt CER practices. However, relying solely on subsidies is insufficient—collaboration through mechanisms such as cost-sharing contracts can further enhance sustainability outcomes when enterprises work together. To facilitate low-carbon construction, the government could provide subsidies for developers' promotional and marketing activities as well as funding for contractors' research and development of sustainable materials and technologies. Financial incentives such as tax breaks and preferential lending for potential homebuyers can also accelerate consumer demand. Ultimately, creating a supportive environment where enterprises proactively pursue CER creates a win–win situation where the BSC becomes more sustainable while firms improve their branding and profitability. The insights from this research highlight the need for a multipronged approach. Governments play a key role through policy and financial support. Realizing the full potential of sustainable construction also requires active participation from developers, contractors, and consumers. By outlining optimal strategies and incentives, this study provides valuable guidance to construction industry stakeholders seeking to implement CER collaboratively. [ABSTRACT FROM AUTHOR]