With rising concerns over climate change and stricter cap-and-trade policies, innovative approaches are required to improve transparency and coordination in carbon-constrained supply chains. This study develops an integrated framework combining game theory and blockchain technology to analyze interactions among conventional and renewable energy producers, retailers, and the government. Competition among producers is modeled using Cournot competition, while producer–government relations are represented as a Stackelberg game. The results show that blockchain adoption enhances carbon traceability, reduces transaction costs, strengthens collaboration across supply chain members, and increases overall profitability. Sensitivity analysis further highlights that optimizing renewable energy adoption and managing blockchain implementation costs can yield substantial economic, environmental, and social benefits. These insights provide valuable guidance for policymakers and supply chain managers in designing effective strategies toward carbon reduction and sustainability.