A stochastic evolutionary game of boosting urban low-carbon development in China

China has made notable strides in developing low-carbon cities through policy formulation, pilot programs, and technological innovation. However, significant challenges remain. This study investigates the strategic choices and interaction mechanisms among enterprises, governments, and the public in the context of urban low-carbon development under environmental uncertainty. Using stochastic evolutionary game theory, we introduce Gaussian white noise into a tripartite evolutionary game model to more accurately simulate the influence of external environmental uncertainties on stakeholder decision-making. Numerical simulation yields several key findings: (1) Active public participation can partially substitute for government regulation; (2) Government subsidy mechanisms exhibit heterogeneity, with excessively high subsidies potentially discouraging public participation; (3) Enterprise behavior is highly sensitive to social losses, and minimizing these losses strongly incentivizes low-carbon initiatives; (4) Public participation is most responsive to enterprise compensation mechanisms; and (5) The effectiveness of government regulation is positively correlated with penalty intensity. To promote urban low-carbon development, it is essential to optimize subsidy structures to reduce heterogeneity, enhance enterprise compensation to increase public engagement, and establish reasonable penalty mechanisms to improve regulatory effectiveness. This study provides a theoretical foundation and policy recommendations to support urban low-carbon development. While the model parameters are primarily based on Chinese cases, future research should incorporate international case studies to enrich empirical data and offer broader insights into the global low-carbon transition.