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.
As global awareness of the environmental impacts of rapid economic and social development continues to grow, addressing extreme climate events has become an urgent challenge for the international community. Phenomena such as global warming, frequent extreme weather events, and rising sea levels have profound implications for ecological systems and present significant challenges to economic and social progress. Against this backdrop, low-carbon development has emerged as a pivotal strategy for combating climate change, garnering broad consensus and commitment from nations worldwide. As the world’s largest developing country and leading carbon emitter, China plays a critical role in global climate governance. In 2020, China announced its ambitious “dual carbon” targets: achieving peak carbon emissions by 2030 and carbon neutrality by 2060. These goals underscore China’s resolve to tackle climate change while imposing new demands and challenges on various industries and regions within the country. Under the framework of the “dual carbon” goals, cities — being the central hubs of economic and social activity — represent one of the primary sources of carbon emissions. Statistical data indicate that urban carbon emissions in China account for over 70% of the national total and continue to rise. During periods of rapid urbanization and industrialization, carbon emissions from key sectors such as transportation, construction, and energy have surged, creating substantial challenges for achieving the “dual carbon” targets. This projection underscores the critical urgency of advancing urban low-carbon transformation. Such transformation requires not only technological and economic adjustments but also addresses complex challenges, including policy design, interest alignment, and behavioral shifts. Therefore, investigating the mechanisms and factors influencing urban willingness for low-carbon development is crucial for designing scientifically grounded policies and fostering urban green transformation.
Complex social, economic, and environmental challenges increasingly demand collaboration across multiple stakeholders or agents. No single actor can effectively tackle issues such as technological innovation, public health crises, or climate change in isolation. Multi-stakeholder partnerships harness diverse expertise, resources, and perspectives to address such complex problems. Indeed, recent global analyses highlight that the need for business leaders, policymakers, and civil society to work together has become ever more critical in confronting today’s grand challenges in a sustainable and equitable manner. This context underpins the importance of researching multi-actor interactive mechanisms: understanding how different actors jointly influence outcomes is both a practical necessity and a significant scholarly endeavor.
However, existing research has not yet fully addressed the theoretical and methodological gaps in multi-actor interaction studies. Many prior studies focus on simplified scenarios or isolated actors, without capturing the complexity of interactive dynamics among multiple agents. For example, Chen and Zhao (2022) note that relatively few studies examine how multi-agent interventions affect interactive processes, with most models considering only two interacting information sources, whereas real cases involve more complex, many-to-many interactions. Moreover, much of the literature relies on theoretical models with limited empirical or simulation validation. This gap is echoed in other domains: recent work on innovation under uncertainty observes that there is a research gap in explaining how multiple actors make interactive decisions, indicating a lack of frameworks to capture such joint decision-making processes. In short, prior research has been insufficient in modeling, methodologically analyzing, and theorizing about multi-actor interactive mechanisms in complex systems. This not only limits academic understanding but also hinders practical guidance for policymakers and organizations dealing with multi-stakeholder situations.
To address these gaps, the present study aims to develop an integrated theoretical framework and analytical approach for multi-actor interaction. The goal is to clarify the dynamic mechanisms by which multiple agents jointly affect outcomes, and to propose a model that overcomes the limitations of earlier two-agent or single-level analyses. The importance of this research question is underscored by its potential to improve both theory (by enriching interaction modeling) and practice (by informing more effective multi-stakeholder coordination). We strengthen the motivation for this study with recent literature support and by pinpointing how our approach diverges from existing works. Figure 1 illustrates the conceptual framework of our research problem and approach. It visualizes the core structure of the study — the key stakeholders involved, their interactions, and the collective influence on the focal outcome — thereby serving as a graphical abstract for the research design.
Figure 1 Conceptual framework illustrating the structure of this study’s research problem, highlighting interactions between key stakeholders and their collective influence on the outcome. The framework guides our analysis by visualizing how different actors contribute to and interact within the system. It underscores the multi-agent interactive mechanism at the core of our research questions.
Building on this framework, we explicitly pose the research questions (RQs) that drive our inquiry. These questions are formulated to target the identified gaps and to emphasize the innovative aspects of our approach. Specifically, the study addresses the following key questions:
RQ1: What are the interactive mechanisms among multiple stakeholders in the target context, and how do these interactions jointly influence the overall outcome?
RQ2: How can a novel theoretical model or method be developed to capture these multi-actor interactions, and what new insights does this integrated approach provide compared to existing single-actor or two-actor models? By investigating RQ1, we seek to uncover the multi-actor dynamics — the way different participants influence each other and the emergent results. RQ2 reflects the study’s methodological innovation: we aim to propose a new modeling framework that incorporates the complex interactions identified in RQ1. These research questions are closely aligned with the study’s contributions, as they combine substantive inquiry into interaction mechanisms with the development of an improved theoretical and methodological approach. To highlight how this research differentiates itself from existing literature, Table 1 summarizes a selection of representative studies related to multi-agent or multi-stakeholder interactions. The table outlines each study’s authors and year, research hypothesis or focus, methodology, research context (subjects), and main conclusions. This structured comparison underscores the progression of knowledge in the field and the specific gap that our study aims to fill. As shown in Table 1, prior works have explored various aspects of multi-actor systems, but none has fully addressed the integrated modeling of multi-actor interactive mechanisms with comprehensive validation. In contrast, our study distinguishes itself by providing a unified framework that accounts for multiple interacting agents and by empirically examining the framework’s implications, thereby contributing a novel perspective to the literature. Table 1. Summary of representative literature on multi-actor interactive mechanisms and related studies, highlighting their hypotheses, methods, contexts, and conclusions (and showing the distinct contribution of the present research in contrast to existing work).
As Table 1 indicates, earlier contributions have laid important groundwork in understanding pieces of multi-actor systems — ranging from public opinion spread to governance and cooperative interventions. Yet, none has delivered a holistic theoretical model combined with empirical validation that encompasses the full complexity of multi-actor interactive mechanisms. This study’s differentiating contribution lies in bridging that gap: we develop a unified framework that synthesizes the strengths of prior approaches (epidemic modeling, game theory, agent-based simulation, etc.) and applies it to a contemporary multi-stakeholder problem with rigorous validation. In doing so, our research not only advances the theoretical modeling of multi-actor interactions but also provides a methodological template for analyzing complex systems with many interdependent participants. The findings are expected to offer novel insights into how coordinated multi-actor efforts can be designed and managed more effectively, thereby extending both the literature and practice in this domain.
In recent years, urban low-carbon development has emerged as a critical strategy for addressing global climate change, garnering significant attention from the academic community. Existing research predominantly focuses on several key areas, including: evaluating policy effectiveness, measuring carbon emissions and analyzing their impact mechanisms, fostering technological innovation and digital transformation, devising low-carbon urban planning and development strategies, promoting green finance, assessing carbon emission efficiency, advancing innovative technologies and smart low-carbon practices, exploring pathways to achieve carbon peaking and carbon neutrality, and investigating policy implementation and governance mechanisms. Among these research areas, policy effect evaluation serves as a critical tool for assessing the effectiveness of low-carbon policies.
Zhu and Rao using the Propensity Score Matching-Difference-in-Differences (PSM-DID) model, confirmed that the low-carbon city pilot policy significantly improved the level of carbon reduction. However, Khanna et al. identified policy inadequacies as significant constraints on progress when evaluating low-carbon pilot city programs across eight Chinese cities. Chen et al. through a fixed effects model, revealed a negative correlation between the intensity of low-carbon policies and carbon reduction, suggesting the presence of complex interactive relationships during policy implementation. Furthermore, Zhang et al. demonstrated that financial technology significantly enhanced carbon emission efficiency, underscoring the pivotal role of technology in determining policy outcomes.The study of policy implementation and governance mechanisms examines the effectiveness and optimization pathways of low-carbon policies in practical applications. Through an analysis of low-carbon pilot city policies, found that these policies effectively curbed the financialization of listed companies and promoted real economic development. Wu et al. utilizing statistical data, observed a reduction in carbon emission intensity in the livestock industry in western China, though notable disparities were evident among cities. Similarly, based on the national big data comprehensive pilot policy, demonstrated that technology-driven business model innovations could significantly reduce China’s carbon emissions. Meanwhile, through interviews on six urban governance practices in India, concluded that while new urban governance approaches hold promise, their effectiveness is hindered by the absence of mandatory regulations.The study of carbon emission measurement and impact mechanisms focuses on accurately assessing urban carbon emissions and identifying their driving factors.
Bi et al. developed a greenhouse gas emission inventory for Chinese cities, concluding that industrial energy consumption remains the primary source of emissions.Using multimodal travel data, demonstrated significant emission reduction potential through the coordinated development of public transportation systems. In contrast, Heinonen and Junnila found that urban density has an insignificant impact on carbon emissions, emphasizing the need to incorporate more complex factors into urban planning and development strategies.Technological innovation and digital transformation are widely regarded as critical drivers for improving carbon emission efficiency and advancing low-carbon development.
Cao et al. demonstrated that digital intelligence transformation significantly reduces the carbon emission intensity in the manufacturing sector. Wang et al. revealed that digital technological innovation not only enhances carbon emission efficiency but also produces spatial spillover effects. Chen and Xu found that the development of regional digital economies significantly boosts the green total factor productivity of enterprises. Furthermore, Xu et al. confirmed that green finance and digital inclusive finance work synergistically to promote sustainable economic development.
The urbanization process has a complex impact on carbon emissions, as it can drive economic growth while simultaneously exacerbating carbon emissions. Khan and Su analyzed urbanization levels in emerging industrial countries and identified an optimal level of urbanization for reducing emissions. Xu et al. using data from the Pearl River Delta, found that economic urbanization had the most significant impact on carbon emissions. Yu et al. employing the STIRPAT model with data from the Yangtze River Delta urban agglomeration, revealed a negative correlation between city size and carbon emissions. Similarly, Song et al. using provincial data from China, showed that urbanization does not necessitate completely eliminating energy consumption to align with low-carbon development goals. Lin and Li analyzing city-level data from the Guangdong-Hong Kong-Macau Greater Bay Area with the STIRPAT model, also found a negative correlation between low-carbon development and the level of new urbanization.The study of urban agglomeration synergy and regional development highlights the critical role of regional cooperation and integration in achieving low-carbon goals. Jiang et al. using social network analysis with data from cities in the Pearl River Basin, demonstrated that regional cooperation effectively facilitates low-carbon development. Feng et al. through panel data analysis of 279 Chinese cities, confirmed that regional integration significantly reduces carbon intensity. Wei and Zheng found that the carbon emission intensity in the Guangdong-Hong Kong-Macau Greater Bay Area is strongly influenced by economic development and urbanization processes. Similarly, Wei et al. identified multiple factors, including economic and industrialization considerations, as key drivers of carbon emissions in urban agglomerations, underscoring the need for a comprehensive and multidimensional approach to low-carbon development.
The planning and policies of urban transportation systems have a significant impact on carbon emissions. Cui et al. using a life cycle assessment method, evaluated the carbon footprint of Xiamen’s public transportation system and found that the BRT system’s carbon emissions were substantially lower than those of the NBT system. Banister in his analysis of urban transportation and climate change, argued that the current high-mobility model is unsustainable and advocated for the adoption of low-carbon transportation systems. Menichetti and Vuren examined the needs and challenges of modeling sustainable transportation systems in Masdar City, Abu Dhabi, highlighting the importance of incorporating electric transportation options. Similarly, Sobrino and Arce analyzing 2149 travel surveys from the Technical University of Madrid, revealed that private transportation modes accounted for over 55% of commuting-related carbon dioxide emissions.
Green finance is widely recognized as a critical tool for advancing low-carbon transformation. Using urban data from Jiangsu Province, found that green bonds significantly reduced carbon emission intensity. Employing a multi-stage difference-in-differences model, demonstrated that green finance reform significantly accelerated the transition to low-carbon energy. Wang and Gao through a difference-in-differences model, revealed that green finance policies substantially improved the welfare performance of low-carbon economic regions. Xu et al. confirmed that green finance, in conjunction with digital inclusive finance, synergistically promotes sustainable economic development. Similarly, Zhang et al. analyzing provincial panel data with mediation effect and GMM models, concluded that green finance plays a pivotal role in the low-carbon transformation of the economy. The assessment of carbon emission efficiency seeks to evaluate how effectively cities manage carbon emissions amidst economic growth. Guo and Wang using the progressive difference method based on China’s smart city pilot policy, found that smart city construction significantly reduced per capita CO emissions. Zhu et al. leveraging high-resolution satellite data and a stratified difference method, demonstrated that the carbon emissions trading system effectively mitigated economic inequality in developing countries. Gao et al. using prefecture-level city data and the difference-in-differences method, found that China’s carbon market policy fosters the convergence of carbon shadow prices. Additionally, Deng et al. constructed a bi-level multi-objective optimization model to validate carbon reduction strategies in Shenzhen’s food waste treatment system, enabling enterprises to cut emissions by over 50%.
Industry is a major contributor to urban carbon emissions, making industrial transformation essential for achieving low-carbon goals. Yang and Chen through a quantitative analysis of industrial carbon emissions in Chongqing, identified industrial output as the primary driving factor. Zhang et al. using data from the Yangtze River Delta region, revealed varying degrees of decoupling between industrial carbon emissions and economic growth. Shao et al. employing the logarithmic mean Divisia index decomposition method to analyze industrial carbon emissions in Tianjin, concluded that improving energy efficiency is key to reducing emissions. Liu et al. through scenario analysis of Suzhou’s low-carbon city transformation, determined that economic structural adjustments are more effective than technological upgrades. Lu et al. integrated the WFA and MFA methods to construct the ISSWFMA model, highlighting how industrial symbiosis enhances resource recycling and supports low-carbon city development. Similarly, Kim et al. using input-output analysis of South Korea’s eco-industrial park projects, found that these initiatives promoted production, value addition, and significant job creation. Moreover, most studies inadequately address the systematic interactions among governments, enterprises, and the public, lacking a comprehensive analytical framework. For instance, The impact of the digital economy on land-use transformation but failed to consider the collaborative effects of multiple agents. Additionally, the exploration of the formation mechanisms behind low-carbon development willingness is insufficient, particularly regarding the influence of external environmental uncertainties. Liu et al. analyzed the direct effects of climate finance on carbon emission efficiency but lacked a systematic approach to the complex decision-making processes involved.
While several studies have employed game theory to analyze low-carbon development, our research distinctively differs from similar works in the literature. For instance, Fu and Wang focused on blockchain technology’s application in low-carbon cities, using a deterministic model that does not account for environmental uncertainties. In contrast, our study incorporates stochastic elements through Gaussian white noise, enabling a more realistic simulation of decision-making under uncertainty. Similarly, He et al. applied a tripartite evolutionary game model to analyze the Chinese Certified Emission Reduction scheme, but their model was deterministic and focused specifically on carbon market mechanisms rather than broader urban low-carbon development. Our study extends beyond these approaches by: (1) incorporating stochastic elements to model environmental uncertainties, (2) focusing on the willingness for low-carbon development rather than specific technological solutions or market mechanisms, (3) analyzing the substitution effect between government regulation and public participation, and (4) examining the heterogeneity in subsidy mechanisms and their impact on stakeholder behavior. This unique approach provides novel insights into the complex dynamics of urban low-carbon development that were not captured in previous studies.
Building on the identified research gaps, this paper seeks to construct a stochastic evolutionary game model involving the government, enterprises, and the public under uncertain environmental conditions, employing stochastic evolutionary game theory. The study systematically analyzes the strategic choices and evolutionary mechanisms of these entities in the process of urban low-carbon development. Specifically, it incorporates external environmental uncertainties, representing their impacts on decision-making through stochastic variables such as Gaussian white noise. This approach aims to uncover the evolutionary paths and equilibrium states of various entities’ strategies in a dynamic environment. The research will utilize stability theory to determine the model’s equilibrium solutions and employ numerical simulations to explore the sensitivity of key parameters on evolutionary outcomes. These findings will inform the development of more scientific and systematic policy recommendations. The innovation of this paper lies in its application of stochastic evolutionary game theory to the study of urban low-carbon development, addressing methodological and mechanism analysis gaps in existing research. By adopting a multi-agent interaction perspective, the study unveils the synergistic roles and dynamic evolutionary processes of governments, enterprises, and the public in the low-carbon transition. The findings not only contribute to the theoretical enrichment of decision-making models for low-carbon development but also provide a scientific foundation for devising more effective urban low-carbon policies. This research supports China’s efforts to achieve its “dual carbon” goals and fosters the sustainable development of cities.
The main research content of this paper includes: constructing a tripartite stochastic evolutionary game model with Gaussian white noise, depicting the impact of the external environment on the decision-making of agents; analyzing the equilibrium solutions of the model based on stability theory, and exploring the evolutionary paths of strategy choices for each agent; using numerical simulations to analyze the impact of key parameters on evolutionary outcomes, and proposing targeted policy recommendations. The research aims to reveal the dynamic evolutionary mechanism of multi-agent decision-making in urban low-carbon development, analyze the impact mechanism of external environmental uncertainty, and propose systematic policy recommendations to promote urban low-carbon development. The research methods mainly involve stochastic evolutionary game theory, stability analysis, and numerical simulation combined with empirical research. The research conclusions indicate that the randomness of the external environment significantly affects the strategy choices of agents; the rational design of government subsidies and penalty mechanisms, the improvement of enterprise compensation mechanisms, and the enhancement of public participation are key factors in promoting urban low-carbon development; a multi-level policy support system needs to be constructed to drive urban low-carbon transformation. This study not only enriches the theoretical framework of low-carbon city research but also provides a scientific basis for formulating more effective low-carbon development policies, holding significant theoretical value and practical significance for promoting China’s achievement of the “dual carbon” goals.
The following is a description of the paper’s organizational structure. The second part presents a tripartite evolutionary game system model for low-carbon urban development in China, including the national government, enterprises, and the public. The third part also examines the evolutionary stable strategies established by these stakeholders. The fourth part showcases numerical simulations, demonstrating the effectiveness of evolutionary stable strategies under different scenarios. Additionally, this section explains the impact of parameters on these strategies. The fifth part proposes suggestions for the paper’s conclusions.
