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Transitioning to low-carbon energy is key for reaching carbon neutrality and modernizing our energy systems, but it presents significant cost-related challenges for energy businesses. To foster optimal outcomes, this paper develops a game model including power generators, high-energy businesses, and consumers in the carbon trading framework. The model explores how different entities evolve their low-carbon strategies under social learning influence to optimize utility. Stability analysis of strategy and simulation experiments reveal the following findings: (1) Greater carbon quotas reduce power generators' low-carbon transition willingness while high-energy-consuming enterprises and consumers remain unchanged. (2) Higher prices for low-carbon products offered by high-energy-consuming enterprises boost low-carbon transition motivation across all parties. (3) Increased green premiums enhance revenue for all parties but are constrained by policy and carbon pricing. (4) Both direct and indirect increases in carbon emissions negatively impact the revenue and utility for all stakeholders. (5) Increasing social learning effect fosters a shift towards low-carbon strategies, accelerating the attainment of game equilibrium, and enhancing market stability and sustainability. This research provides decision support for carbon trading policy design and low-carbon transition of energy enterprises. [ABSTRACT FROM AUTHOR]