As the world's largest energy consumer and carbon emitter, China has undertaken a series of low -carbon policies. However, its top -down authoritarian governance, coupled with economic decentralization, challenges policy effectiveness. To facilitate the implementation of incentive -compatible carbon emission reduction policies, this study proposes a tripartite stochastic evolutionary game model involving the central government, local governments, and enterprises. Replicator dynamic equations are then employed to assess how uncertainty shapes participants' behavioral choices. Furthermore, a real -case example validates the theoretical findings and supports subsequent arguments: (1) initial strategy choices by stakeholders influence their transitions but have minimal long-term impact on the final convergence pattern; (2) stakeholders' dedicated efforts, especially central government supervision, shape evolutionary outcomes during policy implementation; (3) the escalation of penalties contributes to policy execution, while transfer payment allocation warrants thorough evaluation as it affects the strategies of both local governments and enterprises; and (4) the incorporation of random elements introduces disruptions in stakeholder evolutionary paths, resulting in deviations and fluctuations from expected patterns. This study not only highlights the importance of resolving the dilemma in implementing emission reduction policies through effective coordination among stakeholders but also reduces uncertainty related to unobserved factors, ensuring a comprehensive range of game outcomes.