Evolutionary Analysis of Multi-Agent Interactions in the Digital Green Transformation of the Building Materials Industry

Abstract

Driven by the “dual carbon” goal and the strategy for cultivating new productive forces, China’s economy is undergoing a crucial transformation from high-speed growth to high-quality development. As a typical high-energy consumption and high-emission sector, the green and low-carbon transformation of the building materials industry directly affects the optimization of the national energy structure and the realization of ecological goals. However, traditional building material enterprises generally face practical challenges such as low resource utilization efficiency, insufficient digitalization and greening integration of the industrial chain, and weak green innovation momentum. The transformation actions of a single entity are difficult to break through systemic bottlenecks, and it is urgently necessary to establish a dynamic evolution mechanism involving multiple entities in collaboration. This paper aims to explore the evolutionary rules and stability of digital green (DG) transformation strategies of building materials enterprises (BMEs) under multi-agent interactions involving government, universities, and consumers. Centering on BMEs, a four-party evolutionary game model among the government, enterprises, universities, and consumers is constructed, and the evolutionary processes of strategic behaviors are characterized through replicator dynamic equations. Using MATLAB R2022 (Version number: 9.13.0.2049777) bnumerical simulations, this study investigates how key parameters, such as government subsidies, penalty intensity, and consumers’ green preferences, affect the transformation pathways of enterprises. The results reveal that the DG transformation behavior of BMEs is significantly influenced by governmental policy incentives and universities’ knowledge innovation. Stronger subsidies and penalties enhance enterprises’ willingness to adopt proactive DG strategies, while consumers’ green preferences further accelerate transformation through market mechanisms. Among multiple strategic combinations, active DG transformation emerges as the main evolutionarily stable strategy. This study provides a systematic multi-agent collaborative analysis framework for the transformation of BME DG, revealing the mechanisms by which policies, knowledge, and market demands influence enterprise decisions. Thus, it offers theoretical and decision-making references for the green and low-carbon transformation of the building materials industry.

1. Introduction

Under the dual drive of the “dual carbon” goals and the strategy for fostering new quality productive forces, China’s economy is in critical transition from high-speed to high-quality growth. As a typical high-energy-consumption and high-emission industry, building materials enterprises (BMEs) play a crucial role in achieving green and low-carbon transformation. In the field of cement production alone, BMEs account for approximately 8% of global carbon dioxide emissions, making them a key target for the low-carbon transformation efforts [1]. With the development of the industrial technological revolution, digital green (DG) is a new development model that combines digital technologies such as big data, artificial intelligence and the Internet of Things with the green development concept [2]. It follows the dual logic of “green empowerment of digitalization” and “digitalization leading green development”, deeply integrating digital technologies with the entire life cycle of building materials (including raw material extraction, production processing, and building application, as well as recycling and reuse, etc.) throughout the industrial chain. It achieves energy efficiency improvement, carbon accounting optimization, and collaborative green innovation within the industry, thereby reducing the environmental footprint of digital infrastructure itself and maximizing the green benefits of digital technology application. It has become an urgent task for building material enterprises to DG transform and upgrade [3]. However, traditional BMEs generally face problems such as low resource utilization efficiency, insufficient DG integration across the industrial chain, and weak motivation for green innovation, which make it difficult to advance DG transformation in a coordinated manner [4]. In the context of complex and diverse interest structures, how to construct a dynamic evolution mechanism that integrates digital empowerment and green low-carbon transformation has become a core issue of concern for both the academic community and policy makers.

In the past few years, the rapid development of DG technology has created unprecedented new opportunities for BMEs’ green transformation. The deep integration of new-generation information technologies such as big data, artificial intelligence, and the Internet of Things with DG technology not only significantly enhances the accuracy of resource and element optimization allocation and the real-time nature of environmental monitoring from a technical perspective but also promotes information transparency and collaborative development by breaking down data barriers between the upstream and downstream of the industrial chain, compelling the production end to practice green manufacturing standards. Guiding the consumer end to form a consensus on low-carbon consumption has, in turn, accelerated the profound transformation of the entire chain of green production and consumption patterns. However, BMEs’ DG transformation is by no means a solo performance by a single entity. Rather, it is a systemic transformation that requires the in-depth participation and collaborative efforts of four core stakeholders: the government, enterprises, universities, and consumers [5]. As the top-level designer, the government has created a stable and orderly policy environment for the transformation process by introducing incentive policies such as special subsidies and tax reductions, as well as formulating strict industry environmental protection standards and regulatory details. As the key implementer of transformation, enterprises shoulder the heavy responsibility of technology implementation and model innovation. They need to proactively assume the dual risks of R&D investment and market expansion, and they must seek a sustainable development path in the balance between economic benefits and environmental benefits. Consumers, based on their green preferences and purchasing choices, have established a market-oriented feedback mechanism, forcing enterprises to accelerate the pace of green transformation [6]. What is particularly crucial is that universities, as independent entities, have been incorporated into the stakeholder framework of BMEs’ green transformation, which holds irreplaceable strategic significance, and their value far exceeds the mere dimensions of technology and talent supply. On the one hand, universities are the core bases for DG’s fundamental research and cutting-edge innovation in technology. Relying on their strong scientific research capabilities and talent reserves, they can overcome the key technical bottlenecks in BMEs’ green transformation, provide original and high-value-added technical solutions for enterprises, and at the same time cultivate compound talents with both professional technical capabilities and green development concepts. They inject continuous intellectual momentum into the transformation. On the other hand, universities play the role of a bridge for collaborative innovation among industry, academia and research. By building platforms for cooperation between universities and enterprises and jointly establishing research and development centers, they effectively connect the technological achievements of laboratories with the actual demands of the industrial end, shorten the technology transformation cycle, and solve the industry pain point of “difficulty in the implementation” of scientific and technological achievements. In addition, universities, with their academic neutrality and professional authority, can deeply participate in the formulation of technical standards and evaluation systems related to BMEs’ green transformation, promoting the industry to move from decentralized development to standardized and regulated development. The interaction among these four major actors is not a simple linear connection but rather presents a complex game and symbiotic relationship. The dynamic evolution of their interests and strategic choices directly determines the advancement speed and ultimate outcome of BME DG’s transformation.

2. Literature Review

In recent years, research on DG transformation has become a prominent topic in both academia and practice, while the DG development of BMEs has emerged as an urgent priority for China’s economic and social transformation. Scholars have paid extensive attention to this issue, and existing studies on the DG transformation of BMEs can be broadly categorized into several areas.

2.1. Research Trends of Digital Green Transformation in the Building Materials Industry

Existing research on DG transformation in the building materials industry mainly focuses on technology empowerment, transformation paths, and multi-subject collaboration, providing important theoretical and practical references for the construction of this model. However, there are still deficiencies in systematically integrating multi-subject interests and dynamic evolution mechanisms.

2.1.1. Technology-Empowerment-Oriented Research

This type of research focuses on how digital technology and green technology jointly empower the transformation of the building materials industry, exploring the application effects and action mechanisms of various technologies. For example, Virmani et al. (2025) used the TOE framework and institutional theory to analyze the adoption of green hydrogen in the automotive industry, identifying government policies and skilled labor as key driving factors, which provides a reference for incorporating policy and technology factors into the game model of the building materials industry [7]. Setyadi et al. (2025) integrated circularity, localization, and digital resilience at multiple levels, emphasizing the interdependence of technological systems, which inspires the design of the linkage mechanism between digital and green technologies in the building materials industry model [8]. Sreenu (2025) [9] and Abbas & Najam (2025) [10] verified the role of digital finance in promoting green innovation through panel data analysis, revealing the financial support mechanism behind technological transformation, which provides a basis for setting cost and benefit parameters related to the transformation of BMEs. Hidayat-ur-Rehman and Hossain (2025) [11] explored the impact of Fintech adoption on banks’ sustainable performance, and their analysis of regulatory effects provides a reference for the design of government regulatory mechanisms in the model. Chen et al. (2025) [12] studied the spatial and temporal effects of the integration of digital and green finance on carbon reduction, highlighting the synergistic effect of policies and markets, which provides a basis for the setting of government policy tools. Barbieri and Capoani (2025) emphasized the combination of government-led long-term strategies and digital technology applications, further confirming the core role of policies and technologies in transformation [13]. Koul (2025) [14] and Alquraish (2025) [15] reviewed the application of smart technologies, such as the Internet of Things and artificial intelligence, in green manufacturing, pointing out technical bottlenecks such as high initial investment, which helps to reasonably set the transformation cost parameters of enterprises and universities in the building materials industry. Zhang et al. (2025) emphasized the role of intelligent technologies in promoting green practices and carbon reduction, further consolidating the core position of technology empowerment in the model [16].

2.1.2. Transformation Path-Oriented Research

This type of research focuses on exploring the specific implementation paths and influencing factors of DG transformation in the building materials industry and constructs decision models based on industry characteristics. Asif et al. (2024) studied the impact of digital transformation and corporate culture on sustainable performance in the manufacturing industry, finding that innovation capability plays an intermediary role, which provides a reference for setting the strategic choice logic of BMEs in the model [17]. Azman et al. (2025) analyzed the impact of market competition on the productivity of construction enterprises, revealing the regulatory role of market factors on enterprise strategic choices, which helps to design the market benefit mechanism in the model [18]. Akin and Akin (2025) explored the driving factors of green investment in the UK real estate industry, pointing out the key role of regulatory frameworks and market demand, which provides empirical support for defining the benefit functions of the government, enterprises, and consumers [19]. Jesus et al. (2024) conducted a case study on ESG practices of Brazilian construction enterprises, finding that enterprises focus on environmental dimensions but lack transparency, which provides a realistic reference for setting the passive transformation behavior of BMEs in the model [20]. Clarke et al. (2023) developed tools related to net-zero carbon buildings, emphasizing the importance of design guidance, which provides a basis for setting the technical support and standard-setting functions of universities in the model [21]. AlJaber et al. (2023) systematically sorted out the barriers and driving factors of circular economy transformation in the building sector, pointing out the synergistic effect of strict governance and technological innovation, which provides a reference for the design of constraints for multi-subject collaboration in the model [22]. Bormon et al. (2025) evaluated the application effects of green and low-carbon building materials, emphasizing the supporting role of digital tools such as BIM, which provides a specific direction for setting the technical cooperation content between enterprises and universities in the model [23]. Xia et al. (2024) analyzed the synergistic effect of digital transformation and green innovation in the construction machinery industry, and their analysis of non-linear relationships and regulatory effects provides a reference for constructing the dynamic evolution mechanism of multi-subject strategic interaction in the model [24]. Wang et al. (2025) verified through the Baoding case that policy systems and digital platforms can effectively promote the popularization of green building materials, which provides a practical basis for the design of government regulation and subsidy mechanisms [25]. Magaletti et al. (2025) studied the ESG driving factors for decarbonization in the global building sector, providing a reference for setting variables such as consumers’ green preferences and enterprises’ social responsibility in the model [26]. Shanbhag and Dixit (2024) constructed a dynamic life cycle assessment framework, providing ideas for quantifying parameters such as carbon emission reduction benefits in the model [27].

2.1.3. Multi-Subject Collaboration-Oriented Research

This type of research focuses on the collaborative relationship among multiple subjects in the transformation process of the building materials industry, exploring the interaction mechanism between different subjects. Napiontek et al. (2025) analyzed the carbon emission trends of building materials in German cities, providing data reference for setting parameters such as carbon emission reduction costs and benefits in the model [28]. Zhao et al. (2025) constructed a tripartite framework of “technology–reputation–policy” for green building adoption, analyzing the interaction between the government, enterprises, and consumers, which lays a foundation for expanding the quadruple game in this paper but lacks the participation of universities as key technical supply subjects [29]. Barbhuiya et al. (2025) reviewed low-carbon building materials for sustainable pavements, providing a reference for setting the technical paths and benefits of enterprise transformation in the model [30]. Yin and Zhao (2024) constructed an agent-based evolutionary game model for the transformation of the building materials industry to green intelligence, emphasizing the role of government regulation, whose modeling logic and parameter setting provide direct reference for this paper but fail to clearly incorporate the market feedback role of consumers [31]. Fishman et al. (2024) studied global building material intensity data, providing a basis for setting parameters such as material production costs in the model [32]. Zhu et al. (2024) analyzed the implementation path of China’s energy policy for the “dual carbon” goal, providing a policy basis for the design of government policy tools in the model [33]. Bashir et al. (2024) investigated the application status of green building materials in the Pakistani construction industry, revealing practical constraints such as insufficient market demand and high costs, which provides a reference for setting consumers’ purchasing behavior and enterprises’ transformation costs in the model [34]. Martinez-Rocamora et al. (2024) used clustering technology to identify building types, providing ideas for setting differences in consumer preferences under different scenarios in the model [35]. Bezerra et al. (2024) pointed out the challenges of ESG implementation in the Brazilian construction industry, providing a reference for the design of constraints for multi-subject collaboration in the model [36]. Liu et al. (2024) constructed a tripartite evolutionary game model for greenwashing governance in green financial products, whose benefit matrix design and stability analysis methods provide direct reference for the construction of the quadruple game model in this paper, but they do not involve the technical cooperation interaction between universities and enterprises [37].

2.2. Research on the Evolutionary Game of Digital and Green Transformation in the Building Materials Industry

Existing research on evolutionary games related to DG transformation in the building materials industry mainly focuses on two-party or tripartite static games, and there is a lack of dynamic evolutionary game analysis involving multiple subjects such as universities, which provides a space for the innovation of this model.

2.2.1. Two-Party Evolutionary Game Research

Most of these studies focus on the game relationship between two core subjects, such as government–enterprises and enterprises_consumers, exploring the equilibrium state of their strategic choices. For example, Yin and Zhao (2024) [31] constructed an agent-based evolutionary game model for the transformation of the building materials industry to green intelligence, focusing on the game between the government and enterprises, analyzing the impact of government regulation intensity and financial support on enterprise transformation behavior, which provides a reference for the setting of game parameters between the government and enterprises in this paper. However, this model ignores the technical support role of universities and the market feedback role of consumers, resulting in an incomplete game subject system. Bashir et al. (2024) [34] indirectly reflects the game relationship between enterprises and consumers through the investigation of the application status of green building materials, finding that consumer demand is an important factor affecting enterprises’ adoption of green materials, which provides a basis for setting the game mechanism between enterprises and consumers in the model.

2.2.2. Tripartite Evolutionary Game Research

This type of research expands the game subjects to three parties, enriching the interaction mechanism of the model. For example, Zhao et al. (2025) [29] constructed a tripartite evolutionary game framework of “technology–reputation–policy” for green building adoption, involving the government, enterprises, and consumers, analyzing the synergistic effect of various factors on green building adoption. This provides a reference for the interaction mechanism design between the three parties in this paper but lacks the participation of universities, making it impossible to reflect the technical support and talent supply in the transformation process. Liu et al. (2024) [37] constructed a tripartite evolutionary game model for greenwashing governance in green financial products, involving regulators, enterprises, and investors, whose model construction method and stability analysis process provide a reference for this paper, but the research field is green finance, and the applicability to the DG transformation of the building materials industry needs to be adjusted and optimized.

It can be seen that existing evolutionary game research related to the DG transformation of the building materials industry has the following deficiencies: First, the coverage of subjects is incomplete, and none of the studies include universities as independent subjects in the game framework, ignoring their key roles in technological innovation, talent cultivation, and knowledge transfer. Second, the interaction mechanism is simplified, mostly focusing on static game analysis of two or three parties, lacking the exploration of long-term dynamic evolution processes such as strategic adjustment, learning effects, and interest game iteration among multiple subjects. Third, the research perspective is relatively single, failing to systematically integrate policy incentives, knowledge supply, and market feedback to construct a unified multi-subject collaborative analysis framework. These gaps provide a realistic basis for the construction of the quadruple evolutionary game model in this paper.

2.3. Research on the Diversified Participants in the Digital and Green Transformation of the Building Materials Industry

Based on the above research trends and gaps, this paper includes the government, BMEs, universities, and consumers into the quadruple evolutionary game model. The direct argumentation for the inclusion of each subject and the supporting literature are as follows.

2.3.1. Government: Leading Subject of Policy Guidance and Institutional Supply

The government, as the top designer of national economic development strategies, undertakes the core functions of policy formulation, incentive constraints, and regulatory oversight in the DG transformation of the building materials industry, and its strategic choices directly affect the transformation motivation of other subjects. Existing studies have fully confirmed that government policies such as subsidies, tax incentives, and environmental regulations are key external driving factors for enterprise transformation [25,31]. For example, Wang et al. (2025) [25] verified through the Baoding case that the government can effectively promote the popularization of green building materials through policy systems such as pilot projects and digital platforms. Zhu et al. (2024) [33] pointed out that China’s energy policy framework provides institutional support for industrial transformation. In the game model, the government’s strategic choices of “strict regulation” and “lenient regulation” directly affect the cost–benefit structure of enterprises and universities through parameters such as subsidies (α, β, γ) and penalties (λ, μ), and its regulatory costs and credibility losses (Z) constitute the constraints of its own strategic choices. Therefore, including the government in the model is the key to reflecting the guiding role of policies in the transformation process and filling the gap caused by an insufficient focus on a combination of policy mechanisms and multi-subject interaction in existing research.

2.3.2. Building Materials Enterprises: Core Implementer of Transformation Practices

Enterprises are the direct undertakers of DG transformation, and their strategic choices of “active transformation” and “passive transformation” determine the actual progress and effect of industrial transformation. They are the core link connecting technology supply (universities) and market demand (consumers). Existing studies have shown that enterprise transformation behavior is affected by multiple factors such as technology feasibility, market benefits, and policy incentives [17,24,34]. For example, Xia et al. (2024) [24] found that the synergistic effect of digital transformation and green innovation of construction machinery enterprises can promote the upgrading of the global value chain; meanwhile, Bashir et al. (2024) [34] pointed out that enterprises lack transformation motivation due to high costs of green materials and insufficient market demand. In the game model, parameters such as enterprise transformation costs (C₁, C₂), market benefits (L₁, L₂), and technology spillover benefits (O₁) directly determine their strategic choices, while cooperation costs with universities (M), breach penalties (F), and government subsidies and penalties constitute important external constraints. Therefore, including enterprises as the core implementers in the model is the basis for ensuring that the model is in line with industrial practice and revealing the core driving mechanism of transformation.

2.3.3. Universities: Core Supply Subject of Knowledge Innovation and Talent Support

Universities are the source of technological innovation and talent training, and they play unique roles in breaking through technical bottlenecks, promoting the transformation of scientific and technological achievements, and formulating industry standards in the DG transformation of the building materials industry. However, their roles have not been fully reflected in existing evolutionary game models. Existing studies have pointed out that the scientific research capabilities of universities and industry–universities–research cooperation can effectively break through technical bottlenecks [14,15]. For example, Koul (2025) emphasized the core role of universities in the research and development and application of intelligent technologies [14]. Alquraish (2025) pointed out that the technical integration between universities and enterprises can improve supply chain sustainability [15]. In the game model, parameters such as university transformation costs (C₃, C₄), government subsidies (βG₁), technology transformation benefits (M), and knowledge spillover effects (O₂) determine their strategic choices of “active transformation” and “passive transformation”, and their technical support directly affects the transformation efficiency of enterprises and the product trust of consumers. Including universities in the model can fill the gap of incomplete subject coverage in existing research and fully reflect the closed-loop logic of “policy guidance–technology supply–industrial implementation–market feedback”.

2.3.4. Consumers: Market-Driving Subject of Transformation Demand Feedback

Consumers are the terminal of the product value chain, and their strategic choices of “DG purchase” and “traditional purchase” constitute the market feedback mechanism for enterprise transformation, affecting enterprise transformation decisions through market benefit signals. Existing studies have confirmed that consumers’ green preferences and purchasing behaviors have a significant impact on enterprises’ green production decisions [34]. For example, Bashir et al. (2024) pointed out that insufficient market demand is a key reason why enterprises are unwilling to adopt green materials [34]. In the game model, consumers’ green preference coefficient (θ), purchase cost (C₅), product benefits (R₁, R₂), and government consumption subsidies (γG₂) directly determine their purchasing decisions and then affect enterprises’ transformation willingness through market benefits. Including consumers in the model can make up for the deficiency in existing studies, which ignore market demand drivers, enabling the model to more comprehensively reflect the transformation mechanism of the collaboration of policies, technologies, and markets.

In summary, the core flaws of the existing research limit the in-depth interpretation of multi-agent interaction: Firstly, the coverage of agents is incomplete. No studies have included “university” in the analytical framework, which ignores the crucial role universities play in technological research and development, talent cultivation, knowledge transfer, etc. As a knowledge supply entity, universities are the core link connecting technological innovation and enterprise practice. Their absence leads to the disruption of the multi-agent interaction chain. Secondly, the interaction mechanism is simplified. Most studies focus on bilateral or tripartite static games, lacking analysis of the long-term strategic adjustments, learning effects, and dynamic evolution of the four main agents. Thirdly, there is insufficient theoretical integration. No unified multi-agent collaborative analysis framework has been constructed, making it difficult to explain the interaction mechanism among policy incentives, knowledge supply, and market feedback, and studies are unable to provide a systematic multi-agent interaction solution for enterprise transformation.

It should be noted that the unique institutional background of China, such as “coordination between the central and local governments” and “industry policy dominance”, may lead to unexpected outcomes in policy implementation, such as central–local goal trade-offs and regional implementation deviations. Moreover, insufficient departmental coordination may result in the failure of policy coordination. All of these need to be considered within a dynamic evolution framework involving multiple interacting entities. To address these gaps, this study integrates evolutionary game theory, DG innovation theory, and multi-stakeholder collaborative governance theory to construct a quadruple evolutionary game model. This study aims to answer the following questions: (1) What are the behavioral motivations and strategic choices of the government, BMEs, universities, and consumers in DG transformation? (2) How do the strategies of the four stakeholders evolve to form stable equilibria? (3) How can policy incentives, knowledge supply, and market feedback achieve synergistic effects?

The research objectives are: (1) to analyze the behavioral motivations and strategy selections of different stakeholders in DG transformation; (2) to depict the evolutionary pathways and equilibrium characteristics of multi-stakeholder interactions; and (3) to provide policy recommendations that promote deep DG development integration in the building materials industry. The findings are expected not only to extend the theoretical boundaries of DG transformation but also to offer practical guidance for high-carbon industries seeking sustainable development.

3. Methodology

3.1. Model Assumptions

The fundamental principle of evolutionary game theory lies in the concepts of evolutionarily stable strategies (ESSs) and replicator dynamics. In an evolutionary game, stakeholders do not have complete information about the game environment or other players’ payoffs. Instead, they make strategy choices based on the principle of self-interest maximization, continuously adjusting their behaviors to maximize their own benefits [38]. Through repeated interactions, the entire game system gradually evolves toward equilibrium. Consequently, evolutionary game theory is widely applied in areas such as environmental governance, collaborative innovation, supply chain behavior evolution, and government regulation [39]. This study focuses on the multi-subject interest game and strategy evolution mechanism in the green transformation process of BMEs. It selects the four-party evolution game model of government–enterprises–universities–consumers as the core analytical tool. The selection basis is mainly based on the following three considerations, aiming to ensure the high adaptability of the model to the research question. Firstly, the four-party game model is in line with the composition of the core participants in BMEs’ green transformation. The DG technology-driven green transformation of BMEs is not an independent action of a single or a few entities but a systematic change involving the participation of four core stakeholders: the government, enterprises, universities, and consumers [12]. Among them, the government undertakes the top-level policy design and regulatory functions, enterprises are the implementation carriers for technology application and green production, universities provide the core driving force for technological research and development and talent support, and consumers form a market-based feedback mechanism through their green consumption preferences. Compared with two-party game models (such as government–enterprise games and universities–enterprise games), which can only analyze the interaction relationships among local subjects, and three-party game models, whose shortcomings include difficulties in taking into account key links such as consumer market feedback and university technology empowerment, four-party game models can fully include all core actors, achieve a true reproduction of real scenarios, and avoid the one-sidedness of research conclusions caused by the omission of subjects [31]. Secondly, the four-party game model meets the analytical requirements of complex interactive relationships. The multi-subject interaction in the green transformation of BMEs presents a closed-loop logic of “policy guidance–technical support–industrial implementation–market feedback”. There is a significant strategic interaction mechanism among the subjects: government subsidies and regulatory policies will directly affect the transformation investment and risk decision-making of enterprises [34]. The technological research and development direction and the efficiency of technology transfer in colleges and universities will change the marginal cost of green production for enterprises. Consumers’ green purchasing choices will in turn restrict the adjustment of enterprises’ production strategies. This multi-directional and dynamic interactive relationship cannot be precisely depicted by two-party or three-party game models—such simplified models often regard the roles of some subjects as exogenous variables, thus severing the intrinsic connections among the subjects [31]. The four-party game model can clearly present the mutual influence paths of the strategy choices of each subject, providing a feasible analytical framework for analyzing the equilibrium state of multi-subject games. Finally, the four-party game model achieves a balance between the integrity of the subject and the accuracy of the analysis. Compared with the generalized multi-party game model that covers more non-core entities, the four-party game model effectively avoids problems such as redundant strategy dimensions and complex equilibrium solutions caused by an excessive number of entities while ensuring full coverage of core entities [35]. In practical scenarios of BMEs’ green transformation, the core driving forces and key constraints are concentrated in four major entities: the government, enterprises, universities, and consumers. If other entities such as industry associations and financial institutions are included, it will not only significantly increase the complexity of the model but also dilute the research focus and reduce the model’s interpretability for core issues [20]. Therefore, the four-party game model is the optimal choice that takes into account both the depth of research and feasibility.

Based on the above analysis, this study will construct a four-party evolutionary game model of government, enterprises, universities and consumers. By setting the benefit functions of each subject and replicating the dynamic equation, the evolutionary stability strategy of the game will be solved, thereby revealing the influence mechanism of multi-subject interest games on the effectiveness of BMEs’ green transformation. The related assumptions are as follows.

3.1.1. Game Stakeholders

In the DG transformation game, there are four participating stakeholders: the government, BMEs, universities, and consumers. All stakeholders are assumed to be boundedly rational, striving to select strategies that maximize their individual payoffs or utility [31]. According to Simon’s core definition, “bounded rationality” refers to the situation where participants have incomplete information, limited cognition, and progressive learning [12]. They cannot exhaust all possible strategies or their benefits. Instead, they adjust their behaviors through experience accumulation and marginal judgment rather than making globally optimal decisions under complete rationality. This is mainly manifested in three key dimensions: First is information incompleteness. Participants cannot obtain the complete strategic choices of other parties in real time (for example, enterprises cannot precisely know the intensity of government regulation, the progress of university research, or the dynamic changes in consumer preferences) and can only adjust their strategies through the accumulation of experience in long-term interactions [32]. Second is cognitive limitations. Participants’ perceptions of benefits have boundaries (for example, enterprises cannot precisely quantify the specific numerical value of reputation benefits, and consumers cannot fully predict the environmental externalities of DG products), and their decisions rely on a simple judgment of “whether the marginal benefit is higher than the marginal cost” [22]. Third is progressive learning. Participants do not reach the optimal strategy all at once but gradually approach a stable state through the replication of the “strategy imitation–benefit feedback–adjustment and optimization” cycle in the dynamic equation, which is fundamentally different from the logical assumption of “achieving Nash equilibrium in one step” under complete rationality [29]. The strategic decision of any stakeholder depends on the strategies chosen by the other three participants. Studying the evolutionary game among these four stakeholders can provide insights into the development trends of BMEs’ DG transformation and help enhance enterprise competitiveness and market positioning.

3.1.2. Strategic Choices of Stakeholders

The government’s strategy set is G {strict regulation G₁, lenient regulation G₂}. In the process of the DG transformation game, the government can adopt strict regulatory policies such as providing financial subsidies, tax incentives, and loan preferences and imposing transition adaptation regulatory requirements for BMEs, universities and consumers to promote the passive DG transformation of BMEs, the active DG transformation of universities and the DG products purchased by consumers. For example, the “Notice of the Ministry of Finance, MOHURD and MIIT on Expanding the Scope of Implementation of the Government Procurement Policy Supporting Green Building Materials” proposes that starting in January 2025, the implementation scope of government procurement policy supporting green building materials will be expanded from the original 30 cities to 101 cities including Chaoyang District of Beijing. The policy covers government investment projects such as hospitals, schools, and affordable housing, embedding the requirements for the use of green building materials throughout the entire process from feasibility study preparation to completion acceptance and encouraging projects to apply for green building labels [40]. The strategy set of BMEs is E {active DG transformation E₁, passive DG transformation E₂}.

The strategy set of BMEs is E {active DG transformation E₁, passive DG transformation E₂}. The BME adheres to cost and risk control principles, prioritizing the adoption of mature and compatible technologies to facilitate the transformation process. It temporarily does not undertake large-scale, cutting-edge research and development investments, focusing instead on short-term benefits and compliant operations. It does not participate in any illegal activities. As the core subject of DG transformation, when BMEs choose to actively carry out DG transformation, they can focus on establishing a deep industry–universities–research collaboration mechanism with universities around “empowering green production with DG technologies” [41]. Colleges and universities can provide key technical support for the DG transformation of BMEs and at the same time cultivate compound talents with “DG technology + green building materials” in a targeted manner [42] to solve the technical problems of BMEs in DG control, green production, intelligent optimization, low-carbon processes, etc. BMEs, on the other hand, provide DG practice scenarios for universities, forming a cooperative closed loop of “DG technology research and development–green scenario application–iterative optimization of achievements”. Conversely, BMEs may also engage in passive DG transformation behaviors. They may disclose core DG transformation technologies developed by universities without authorization or even tamper with DG monitoring data to evade environmental protection supervision. This not only undermines trust in business cooperation but also prevents DG technologies from effectively serving green production, thereby delaying the dual transformation pace of the industry [43].

The strategy set of universities is Q {active DG transformation Q₁, passive DG transformation Q₂}. Colleges and universities focus on the industrial application of existing mature technologies, do not conduct basic research, adapt to the short-term production needs of BMEs to reduce research risks, obtain profits through legal technical services, and adhere to academic integrity and cooperation agreements. In the DG transformation game of the building materials industry, when universities choose to actively carry out DG transformation, they will take the core demand of BMEs for “DG empowering green production” as the guide and provide full-chain DG technical support and resource services [44]. On the one hand, in response to the pain points of green building materials research and development and production for BMEs, a DG research and development platform for green building materials should be established to enhance the level of DG decision-making and management. On the other hand, a focus on the exploration of green demands at the consumer end by leveraging DG technologies such as big data and artificial intelligence to analyze market trends, accurately identify potential consumer demands, and assist BMEs in developing targeted products thereby enhances marketing effectiveness and the market penetration rate of green products. In addition, universities will also deeply respond to the government’s policy orientation of integrating industry, academia and research and jointly build a DG collaborative platform with BMEs. For instance, in accordance with the requirement of “jointly building a DG technology training base” in the “Implementation Plan for DG transformation of the Electronic Information Manufacturing Industry” (2025) [45] issued by the Ministry of Industry and Information Technology and other departments, we will cooperate with BMEs to establish a “Green Building Materials DG transformation Training Center” and cultivate and master compound talents in a targeted manner. Meanwhile, universities will also rely on government-supported innovation platforms to promote the transformation of DG technology achievements and enhance the competitiveness of BMEs in participating in government projects [46]. However, in the process of industry–universities–research cooperation, universities may also engage in passive DG transformation behaviors and encounter issues that violate academic integrity and cooperation contracts. To quickly achieve cooperation targets or obtain research funds, they tamper with experimental data and forge research and development progress to fabricate false technical achievements. Or they may abuse the technology and market data of BMEs to operate in violation of regulations. In government-funded DG industry–universities–research projects, the investment in green technology R&D was falsely reported and special funds were misappropriated for scientific research activities in non-green fields, resulting in the stagnation of DG transformation projects of BMEs.

The consumer’s strategy set is S {DG purchase S₁, traditional purchase S₂}. Consumers are both the starting point and the end point of the DG transformation of BMEs. In the era of the DG economy, the consumer market is shifting from being product-centered to consumer-centered [47]. Guided by the national “dual carbon” policy, supported by the green brand reputation of BMEs and the public opinion guidance of social media, consumers actively tend to choose DG products and thus generate DG purchasing behavior. However, there are also some consumers who have strong traditional concepts and conservative ideas, have a low acceptance of the DG shopping model, and have insufficient understanding of the environmental protection value of green building materials. Traditional building materials have a higher cost performance and are more reassuring to use [48].

The relevant symbols and strategies are defined in

Table 1. Symbols and strategy definitions.

Participants	Strategies	Symbols	Interpretations
Government	Strict regulation	G1	Establish subsidy and penalty policies, set up special funds, strictly enforce environmental protection standards and compliance reviews, including mandatory penalties for violations.
	Lenient regulation	G2	Only collecting normal taxes, without actively providing subsidies or strict supervision, may result in loss of public trust (Z) due to insufficient policy support, and no exemption for punishing violations.
Building materials enterprises (BMEs)	Active DG transformation	E1	Carry out in-depth industry–universities–research cooperation, invest in technological innovation, green production and full-process digital transformation, and strictly abide by contractual agreements and environmental protection regulations.
	Passive DG transformation	E2	Only meeting the basic compliance requirements of the industry, without conducting large-scale research and development, without participating in in-depth cooperation, adhering to the contractual stipulations, without data fraud or illegal disclosure of technology, the core is “low investment and adhering to the bottom line”—a passive form of compliance.
Universities	Active DG transformation	Q1	Carry out research and talent cultivation based on the needs of the enterprise, establish a platform for industry–universities–research cooperation, participate in the formulation of industry standards, and adhere to academic integrity and contractual agreements.
	Passive DG transformation	Q2	Only apply mature technologies to provide services, do not engage in cutting-edge research and development, do not participate in standard setting, adhere to academic integrity, do not tamper with data or divert research funds, strictly fulfill contractual obligations. The core principle is “light on research and development, heavy on compliance”—a conservative approach to cooperation.
Consumers	DG purchase	S1	By choosing digitalized environmentally friendly building materials based on green preferences, one can enjoy government consumption subsidies. The decision-making process is influenced by the product’s compliance and technical credibility.
	Traditional purchase	S2	Prefers traditional building materials, attaches importance to cost-effectiveness, has low acceptance of DG products, and does not involve irrational resistance behavior.

.

Based on this, a game model of “government, BMEs, universities and consumers” is constructed, and its mechanism of action is shown in Figure 1.

3.1.3. Basic Assumptions

Hypothesis 1.

The core participants in the DG transformation game are the government, BMEs, universities, and consumers, totaling four parties. All entities are of bounded rationality and make decisions based on the principle of “marginal benefit > marginal cost”. They gradually approach stable strategies rather than making immediate optimal decisions under complete rationality through the cycle of “strategy imitation–feedback on benefits–optimization adjustment” [22,29]. There is incomplete information among the entities, and they cannot obtain the complete strategies of other parties in real time. However, they can accumulate experience through long-term interaction to adjust their behaviors, and they do not have the strategic inclination of “seeking benefits through illegal means”. All the decisions of the entities are based on the premise of “legal and compliant” [31]. Illegal/moral controversial behaviors such as data fraud, embezzlement of public funds, and unauthorized disclosure of technology do not fall within the scope of the game strategy options. They only exist as “trigger events of breach of contract”. For example, in terms of data fraud, first, when universities and enterprises collaborated on DG technology research and development, they exaggerated the “reduction effect” of the “emission reduction” in the experiments (such as falsely reporting the laboratory emission reduction rate from 30% to 35%) in order to secure subsequent cooperation funds, but they did not tamper with the core experimental principles and key conclusions, and did not violate the “serious circumstances of forging scientific research data” stipulated in the “Interim Provisions on the Handling of Irregular Behaviors in Scientific and Technological Activities”, the activities only being a violation of the performance obligations under the cooperation contract [41]. Second, in the DG transformation of enterprises, in order to meet the “emission reduction indicators” for government subsidies, they slightly adjusted the production energy consumption monitoring data (such as changing the unit energy consumption from 1.2 tons of standard coal per ton of product to 1.1 tons) and did not reach the “serious circumstances of providing false certification documents” stipulated in the “Criminal Law” (did not cause huge losses to the state’s property, did not trigger major safety accidents), only violating the government subsidy application management measures and the enterprise’s internal data management system [45]. Misappropriation of funds: First, universities received government DG transformation special research funds (used for low-carbon material research) and used 5% of the funds to purchase general research equipment (did not exceed the proportion “allowable for moderate use for supporting equipment” stipulated in the “Special Funds Management Measures”), did not reach the “large amount” standard of “embezzlement of public funds” stipulated in the “Criminal Law”, and only violated the “Special Funds Use Rules”. Second, enterprises temporarily used government DG transformation subsidies (designated for the transformation of intelligent production lines) for the digital upgrade of the supply chain (also belonging to the DG transformation-related field), did not change the nature of the fund usage, did not cause the loss of subsidy funds, and only violated the “special funds use agreement” in the subsidy issuance contract [31]. Third, in the universities–industry–research cooperation, universities used the technical service fees paid by enterprises (agreed to be used for the construction of joint laboratories) for DG technology training (belonging to the supporting services of the cooperation), did not infringe upon the enterprise’s interests, and only violated the fund usage agreement in the cooperation contract [47]. Inappropriate disclosure: First, the core DG technology jointly developed by enterprises and universities (not applying for patents, belonging to technical secrets) due to internal management loopholes, disclosed non-core technical parameters to the upstream and downstream enterprises (not affecting the exclusivity of the technology), did not violate the “Anti-Unfair Competition Law” provisions of “infringing upon trade secrets”, and only violated the technical confidentiality agreement signed by both parties [32]. Second, when universities shared DG transformation research results with enterprises in academic conferences without previously obtaining the consent of the enterprises, disclosed some production process data of the enterprises (non-sensitive data, already de-identified), did not infringe upon the enterprises’ commercial interests, and only violated the information disclosure agreement in the universities–industry–research cooperation [29]. Third, in the DG product promotion by enterprises, they disclosed the technical test reports provided by universities (not involving patent technologies and core algorithms) but did not label “technical support from the university”, only violating the intellectual property ownership agreement in the cooperation contract, not constituting an infringement under the “Copyright Law” [17].

Hypothesis 2.

If the government hopes for a “strict supervision” strategy, first, it will establish a special research and development fund G₁ for DG transformation (DGS), providing subsidies to BMEs and universities that actively engage in DGS. Among them, the subsidy coefficients for government investment to BMEs and universities are, respectively, α and β (α and β ∈ [0, 1]). Secondly, when universities and BMEs passively undergo DGS, they will face transition adaptation regulation fee U (this is not a punitive fee; it is for subsequent technological upgrades). This is mainly aimed at entities that have not achieved the phased transformation goals. It is a special adjustment fund provided to support their subsequent technological upgrades, and it is not a punitive measure. The government’s penalties for universities and BMEs’ passive DGS are λ and μ (only for non-compliant negative behaviors, such as failure to complete the basic transformation tasks; λ and μ ∈ [0, 1]). Thirdly, on the basis of the government’s guidance on DG consumption, a special consumption subsidy fund G₂ is set up for consumers. γ represents the subsidy intensity of the government for consumers’ DG consumption. Each consumer who adopts DG purchasing behavior can receive a consumption subsidy γG₂. If the government implements a laissez-faire policy and opts for a “lenient regulation” strategy in the context of DGS, it will gain normal tax revenue T and lose credibility Z due to its lack of support for DGS.

Hypothesis 3.

The DG cost input of BMEs during their active DGS is C₁ (including research and development, as well as equipment investment), the service fee paid to universities is M, the regulatory cost of the government for the active DGS is G₃, the market benefit L₁ which represents the optimistic estimate of the premium for green products by the enterprise is obtained from the increase in the purchase and sales volume of DG building materials, and the social benefit H is brought to the government. In addition, the contract fee serves as a link between BMEs and universities. If a building materials enterprise chooses a passive DGS and violates the contract, although it has not fully fulfilled its cooperation obligations, the university has previously invested technical, theoretical and other knowledge resources to promote the cooperation. From this, the building materials enterprise can obtain the spillover income O₁ (it is not illegal gains but the implicit knowledge transfer that occurs in compliant cooperation) that was not stipulated in the contract. Meanwhile, in accordance with the cooperation contract, BMEs are required to pay the corresponding compensation for cooperative adjustments F to the university as compensation for their breach of contract. The cost for BMEs to adopt a passive DGS strategy is C₂ (only the basic compliance costs; C₁ > C₂), and the sales growth of DG building materials products is limited. BMEs can only obtain market revenue L₂ which represents the conservative estimate of the stable returns in the traditional market (L₁ > L₂) [49], and they need to bear the cost of technical adaptation lag and pay cooperation adjustment compensation to universities. The difference between L₁ and L₂ reflects the “expected deviation” of the enterprise rather than the objective difference in returns. The breach of contract by a BME will prompt the government to incur additional regulatory costs W₁ for regulating market order and coordinating cooperation disputes. If the BME engages in any illegal activities such as data fraud, embezzlement of funds, or unauthorized disclosure during the implementation of any strategy, it will be regarded as a “default event”. This is not a choice made by the strategy itself and will trigger an independent disciplinary mechanism.

Hypothesis 4.

When universities adopt an active DGS, they need to invest more research resources, human resources and other costs, which is C₃ (including basic research and platform construction). If a passive DGS is chosen, the cost will be reduced to C₄ (only the cost of mature technical services; C₃ > C₄). When universities choose the “active DGS” strategy, they will rely on their innovative development capabilities and differentiated value-added services to provide more market opportunities for BMEs, bring value-added benefits K₁ to them, and at the same time promote the application of technology and the supply of talents, bringing social benefits K₂ to the government. In addition, universities will precisely convey product information to consumers through scientific research lectures, education, training, etc., bringing great convenience and speed to consumers and earning their trust benefits K₃. If universities choose the “passive DGS” strategy, it will result in the loss of market trust due to insufficient technical adaptation W₂, increase the regulatory cost W₃ for the government, and cause a loss of consumer perception W₄. Similarly, if universities choose a passive DGS and violate the contract in the cooperation, although they have not fully fulfilled their own obligations, the knowledge resources such as production practice data and industry demand information that the BMEs have already invested in promoting the cooperation will enable universities to obtain spillover benefits O₂ (the transmission of tacit knowledge in compliance cooperation) that have not been stipulated in the contract. It is necessary to specifically point out that the social benefits focus on the positive externalities of the behaviors of the government, enterprises, and universities on the macro-ecology and industrial upgrading (such as the carbon emission reduction contribution of enterprises’ proactive transformation and the industrial empowerment provided by universities’ technology output) [50]; the spillover effect specifically refers to the implicit knowledge transfer benefits that the cooperating entities do not obtain through contractual agreements (such as the inspiration of enterprise production data for university research and the indirect support of university basic research for enterprise technological iteration) [51,52]; the reputation loss is limited to the decline in market trust caused by the entity’s default or negative behavior [53]. According to the cooperation contract, the university is also required to pay the corresponding compensation for cooperative adjustments F to the building materials enterprise as compensation for its breach of contract.

Hypothesis 5.

When consumers choose to purchase from DG, the payment cost is C₅+ θ (θ is the green preference coefficient, reflecting the actual willingness to pay for environmental attributes, influenced by objective information such as product environmental certification and carbon footprint transparency), and the revenue R₁ consists of three parts: ① the environmental value of the product (such as the ecological benefits corresponding to the reduction in emissions); ② the value of digital services (such as full life cycle traceability, construction adaptation guidance and so forth, and practical services); and ③ the government consumption subsidy γG₂. The total revenue is R₁ = environmental value + digital service value + γG₂ − (C₅ + θ). Choosing the traditional purchase, the cost is fixed at C₅, and the revenue R₂ is the basic usage value (R₁ > R₂). The core of the consumer’s decision is to compare “the comprehensive value of DG products (including subsidies)” with “the usage value of traditional products + additional preference cost”, which conforms to the logic of rational consumption. Taking into account the low-frequency and high-value characteristics of construction materials as well as the long decision-making cycle of consumption, consumer behavior is driven by multiple objective factors [31]. In the scenario of new home decoration, consumers pay more attention to environmental friendliness of living and product value-added, and the θ coefficient is higher, indicating a stronger acceptance of DG products; in the scenario of old house renovation, cost sensitivity dominates the decision-making, the θ coefficient is lower, and they are more inclined towards traditional products; in the engineering procurement scenario, it is constrained by tendering policies and enterprise ESG assessment, and the probability of choosing DG products is directly related to policy requirements [23]. In addition, the trust of consumers in DG products depends on university technical endorsements (such as the proof of the transformation of scientific research achievements) and enterprise digital disclosures (such as real-time data of the production process), and this objective information further strengthens the stability of the green preference.

Hypothesis 6.

“The government policy trigger → university technology supply → enterprise transformation practice → consumer market feedback” forms the main closed loop. Government subsidies (α, β, γ) and penalties (λ, μ) are the exogenous core driving forces. The strategies of other entities only interact along this main line to avoid disorderly associations. All the strategic choices of the entities are based on the premise of legality and compliance, focusing on differentiated economic decisions regarding the intensity of transformation investment, the selection of technical paths, and the adaptation of cooperation models. There are no illegal or immoral behaviors set [31,48]. All the funds (subsidies, penalties, adjustment funds) in the model are market-oriented governance tools used to coordinate interests rather than as legal sanctions for illegal acts (legal sanctions have already been reflected through the default penalty mechanism).

Hypothesis 7.

The core stakeholders in this study include four categories: government, building materials manufacturers, universities and research institutes, and end consumers. Suppose the probability of the government choosing strict regulation is p, and the probability of choosing lenient regulation is (1 − p). The probability of BMEs choosing active DGS is x, and the probability of choosing passive DGS is (1 − x). The probability of universities choosing an active DGS is y, and the probability of choosing a passive DGS is (1 − y). The probability of consumers choosing DG consumption is z, and the probability of choosing traditional consumption is (1 − z). Among them, p, x, y and z are all functions of time. Combining the existing literature on group-based single-entity game settings [54,55], the government is defined as a single regional regulatory entity responsible for macro-control actions such as policy formulation and implementation of incentives/punishments. Its strategic choices (strict regulation/lenient regulation) are holistic, continuous, and policy-oriented. Unlike the decentralized decision-making of group entities, the government’s objective function is to maximize the overall regional welfare (including environmental benefits, industrial benefits, and credibility), and strategic adjustments are based on the dynamic assessment of policy implementation effects (such as the trade-off between subsidy costs and emission reduction benefits) rather than individual interest differences [56]. Therefore, the probability of the government choosing strict regulation is set as p (where p is a time-dependent function), reflecting the centralized strategic evolution characteristic of it as a single decision-making unit. Enterprises, universities and consumers are group-type subjects with heterogeneity in strategic choices. There is heterogeneity within these three groups (such as differences in enterprise size, differences in university research capabilities, and differences in consumers’ income and preferences), and their strategic choices are characterized by dispersion, learning, and profit-driven nature [36]. Among them, for the enterprise group, different-sized BMEs have differences in their capacity to bear transformation costs and their ability to acquire technologies. Some leading enterprises may choose “active transformation” first to obtain policy subsidies and market premiums, while small and medium-sized enterprises may choose “passive transformation” due to risk aversion. The probability x (of active transformation) reflects the distribution evolution of strategic choices within the group and conforms to the industrial transformation law of “a few pioneers leading the majority to follow” [33]. For the university group, research-oriented universities and application-oriented colleges have different research orientations. The former tend to “actively transform” to carry out frontier technology research and development, while the latter may focus on the transformation of mature technologies and choose “passive transformation”. The probability y (of active transformation) reflects the differentiated strategic adjustments of the university group based on their own resource endowments [14]. For the consumer group, the green preference coefficient θ shows individual differences (such as young groups with strong environmental awareness and middle-aged and elderly groups with cost sensitivity). The probability z (of DG purchase) reflects the gradual evolution of the market demand side, and its change is influenced by product value, subsidy policies and social cognition, conforming to the “group learning effect” of consumer behavior [57]. Participants tend to imitate the strategies with higher returns within the group (for instance, when the average return of enterprises that actively undergo transformation is higher than that of those that passively undergo transformation, more enterprises imitate E₁) rather than actively calculating the optimal strategy.

Table 2. (a) The relevant parameters and their implications. (b) The basis for parameter settings.

(a)
Variable	Significance	Variable	Significance
G1	The special R & D fund for DG transformation development established by the government when universities and BMEs actively pursue DG transformation	O1	The spillover benefits for BMEs resulting from the DG knowledge input of universities
α	The subsidy level provided by the government for the DG transformation of BMEs	F	The contractual compensation for changes in cooperation terms due to the mismatch in the transformation pace of BMEs and the university, as well as the deviation in technology adaptation, falls within the scope of legal agreements
β	The subsidy extent of the government for the DG transformation of universities	W1	The new regulatory costs for the government due to the “passive DG transformation” of BMEs
U	The transition adaptation regulatory requirements levied by the government on universities and BMEs in the case of their passive DG transformation	C3	The cost of universities taking an active DG transformation
λ	The intensity of the government’s punishment for the passive DG transformation of universities	C4	The cost of universities taking a passive DG transformation
μ	The intensity of the government’s punishment for the passive DG transformation of BMEs	K1	The value-added benefits brought to BMEs by the “active DG transformation” of universities
γ	The government’s subsidy intensity for consumers’ DG purchasing behavior	K2	The social benefits brought to the government by the “active DG transformation” of universities
G2	The government’s special DG consumption subsidy fund for consumers	K3	The trust benefits gained by universities from the “active DG transformation”
G3	The regulatory costs of the government when BMEs and universities actively carry out DG transformation	W2	The compensation for cooperative adjustments due to insufficient technical adaptation due to the “passive DG transformation”
T	The normal tax revenue during the period of the government’s “lenient regulation”	W3	The new regulatory costs for the government due to the “passive DG transformation” of universities
Z	The loss of government credibility during “lenient regulation”	W4	The loss of consumer experience of universities due to the “passive DG transformation”
C1	The cost of DG transformation for BMEs actively engaged in DG transformation	O2	The spillover benefits for universities resulting from the knowledge input of BMEs
L1	The market benefits obtained by BMEs through active DG transformation	θ	Consumers’ preferences for DG products
C2	The DG costs of BMEs during their passive DG transformation	R1	The psychological utility benefits of consumers’ DG purchasing behavior
H	The social benefits brought to the government by the proactive DG transformation of BMEs	J	The social benefits brought to the government by consumers’ DG purchasing behavior
M	The DG transformation service fee paid by BMEs to universities	C5	The costs of consumers’ traditional purchasing
L2	The market gains obtained by BMEs from passive DG transformation	R2	The benefits of consumers’ traditional purchasing
(b)
Parameter Group	Included Variables	Core Theoretical/Empirical Basis
Policy Tools	α , β, γ, G1, G2, U, λ, μ	Rooted in industrial policy theory and Chinese practice: G1 is set with reference to the CNY 1 billion-level transformation funds for the building materials industry in Zhejiang, Anhui, and other provinces; α and β draw on local subsidy standards (e.g., Inner Mongolia’s 20% equipment subsidy for smart factories, Wenjiang District’s 20% subsidy for university DG consulting services); U, λ, and μ are determined based on fine ranges specified in the Data Security Law of the People’s Republic of China and Environmental Protection Law.
Transformation Costs	C1, C2, C3, C4, M, C5	Aligned with innovation cost theory: Based on industry survey data, active transformation involves investments in digital equipment and R&D (C1 > C3), while passive transformation only incurs basic compliance costs (C2 < C4); M is set according to the general level of industry–universities–research cooperation service fees.
Benefits	L1, L2, K1, K2, R1, R2	Guided by market revenue theory: L1 and L2 reflect the premium of green products (surveys show active transformation enterprises achieve 10–30% revenue growth); K1 and K2 correspond to the enterprise value-added and social positive externalities brought by university technological empowerment; R1 and R2 reference empirical research on consumer green product utility evaluation.
Implicit Costs/Benefits	Z , W1, W2, W3, W4, O1, O2, θ	Derived from behavioral economics and knowledge spillover theory: Z represents government credibility loss (based on the policy implementation effect evaluation framework); W1–W4 are implicit costs of default/passive behaviors; O1 and O2 refer to non-contractual knowledge spillover in industry–universities–research cooperation; θ reflects consumers’ green preferences (cited from green consumption behavior empirical studies).

presents the key parameters, their interpretations, and the basis for parameter settings.

3.2. Model Establishment

From the available strategies of the government, BMEs, universities, and consumers, it can be seen that each participating entity has two opposing strategy combinations. Among the four gaming entities, there are 24 = 16 kinds of game strategy combinations. Based on this, the four-party game payoff matrix of the government, BMEs, universities, and consumers is constructed as presented in

Table 3. Payoff matrix.

		Universities Actively Pursue Digital and Green Transformation Q1 (y)		Universities Carry Out Passive Digital and Green Transformation Q2 (1 − y)
		Consumer DG Purchase S1 (z)	Traditional Consumer Purchasing S2 (1 − z)	Consumer DG Purchase S1 (z)	Traditional Consumer Purchasing S2 (1 − z)
The government strictly supervises G1 (p)	BMEs actively embrace digital and green transformation E1 (x)	(G1, E1, Q1, S1)	(G1, E1, Q1, S2)	(G1, E1, Q2, S1)	(G1, E1, Q2, S2)
	BMEs exhibit a passive attitude towards digital and green transformation E2 (1 − x)	(G1, E2, Q1, S1)	(G1, E2, Q1, S2)	(G1, E2, Q2, S1)	(G1, E2, Q2, S2)
The government exercises lax supervision G2 (1 − p)	BMEs actively embrace digital and green transformation E1 (x)	(G2, E1, Q1, S1)	(G2, E1, Q1, S2)	(G2, E1, Q2, S1)	(G2, E1, Q2, S2)
	BMEs exhibit a passive attitude towards digital and green transformation E2 (1 − x)	(G2, E2, Q1, S1)	(G2, E2, Q1, S2)	(G2, E2, Q2, S1)	(G2, E2, Q2, S2)

.

Based on the assumption that when the government selects strategy G₁, the building materials enterprise selects strategy E₁, the university selects strategy Q₁, and the consumer selects strategy S₁, the government’s payoff is K₂ + J + H − βG₁ − γG₂ − G₃, the building materials enterprise’s payoff is L₁ + K₁ + O₁ − F − C₁ − M, the university’s payoff is βG₁ + F + M + K₃ − C₃, and the consumer’s payoff is γG₂ + R₁ − C₅ − θ. Similarly, the other sets of game payoffs for the four parties can be obtained, as shown in

Table 4. The game theory payoff values of the government, BMEs, universities and consumers.

Strategy Combination	Government Revenue	Building Materials Enterprise Revenue	University Revenue	Consumer Revenue
(G1, E1, Q1, S1)	K2 + J + H − βG1 − γG − G3	L1 + K1 + O1 − F − C1 − M	βG1 + F + M + K3 − C3	γG + R1 − C5 − θ
(G1, E1, Q2, S1)	λU + J + H − γG − G3 − W3 − W4	L1 + F +O1 − F − C1 − M	F + M + O2 − λU − W2 − C4 − F	γG2 + R1 − C5 − θ − W4
(G1, E1, Q1, S)	K2 + H − βG1 − G3	L1 + K1 + O1 − F − C1 − M	βG1 + F + M + K3 − C3	R2 − C5
(G1, E1, Q, S)	λU + H − G3 − W3 − W4	L1 + F +O1 − F − C1 − M	F + M + O2 − λU − W2 − C4 − F	R2 − C5
(G1, E, Q1, S1)	μU + J − αG1 − γG − W1	αG1 + L2 − C2 − μU	−C3	γG + R1 − C5 − θ
(G1, E, Q1, S)	μU − αG1 − W1	αG1 + L2 − C2 − μU	−C3	R2 − C5
(G1, E, Q, S1)	μU + J − αG1 − γG − W1	αG1 + L2 − C2 − μU	−C4	γG + R1 − C5 − θ
(G1, E, Q, S)	μU − αG1 − W1	αG1 + L2 − C2 − μU	−C4	R2 − C5
(G, E1, Q1, S1)	K2 + J+T − Z	L1 + K1 + O1 − F − C1 − M	K3 + F + M − C3	R1 − C5 − θ
(G, E1, Q1, S 2)	K2 + T − Z	L1 + K1 + O1 − F − C1 − M	K3 + F + M − C3	R2 − C5
(G, E1, Q2, S1)	J + T − Z	L1 + F + O1 − F − C1 − M	O2 + F + M − W2 − C4 − F	R1 − C5 − θ − W4
(G, E1, Q2, S2)	T − Z	L1 + F + O1 − F − C1 − M	O2 + F + M − W2 − C4 − F	R2 − C5
(G, E2, Q1, S1)	J + T − Z	L2 − C2	−C3	R1 − C5 − θ
(G, E2, Q1, S2)	T − Z	L2 − C2	−C3	R2 − C5
(G, E2, Q2, S1)	J + T − Z	L2 − C2	−C4	R1 − C5 − θ
(G, E2, Q2, S2)	T − Z	L2 − C2	−C4	R2 − C5

.

Based on the initial values in Table 4, taking the strategy combination (G₁, E₁, Q₁, S₁) as an example (strict government regulation + enterprise proactive transformation + university proactive transformation + consumer DG purchase), where government revenue = social revenue (K₂ + J + H)—subsidy expenditure (βG₁ + γG₂) − regulatory cost (G₃) = 2 + 2 + 1 − (0.2 × 10 + 0.3 × 2) − 5 = 5 − 2.6 − 5 = −2.6; enterprise revenue = market revenue (L₁) + university empowerment value (K₁) + technological spillover (O₁) − transformation cost (C₁) − service fee (M) − compensation for cooperative adjustments (F) = 4 + 3 + 2 − 6 − 2 − 1 = 0; university revenue = government subsidy (βG₁) + service fee (M) + trust benefit (K₃) − research and development cost (C₃) + default compensation (F) = (0.2 × 10) + 2 + 1 − 6 + 1 = 0; consumer revenue = government subsidy (γG₂) + comprehensive value (R₁) − basic cost (C₅) − preference cost (θ) = (0.3 × 2) + 5 − 4 − 1 = 0.6. The core revenue of the government is the positive social externality brought to enterprises/universities/consumers (K₂/J/H), while the core cost includes subsidy expenditures (αG₁/βG₁/γG₂) and regulatory costs (G₃/W₁/W₃); the core revenue of enterprises is the premium in the green product market (L₁/L₂) and technological spillover (O₁), while the core cost includes transformation investment (C₁/C₂) and cooperation costs between industry, academia and research (M); the core revenue of universities is government research subsidies (βG₁) and technical service income (M), while the core cost includes research investment (C₃/C₄) and reputation loss (W₂); and the core revenue of consumers is product environmental protection + digital service value (R₁) and government consumption subsidies (γG₂), while the core cost includes purchase cost (C₅) and cognitive preference cost (θ). It should be noted that some combinations, such as (G₁, E₂, Q₁, S₁), have extremely low probabilities in reality. This is because a passive transformation by enterprises (such as tampering with monitoring data) would lead to a loss of consumer trust, making it impossible for the “consumer DG purchase” behavior to occur simultaneously. Moreover, under strict government supervision, a passive transformation by enterprises would face high transition adaptation regulatory penalties (μU) and a negative profit (αG₁ + L₂ − C₂ − μU < 0), and rational enterprises would not choose such an option. Therefore, these combinations are not included in the core analysis.

3.3. Model Solution

Based on the game payoff values of the four parties in Table 4, let U₁₁, U₁₂ and U₁ represent the expected benefits of the government’s S₁ strategy, S₂ strategy and average expected benefit, respectively; let U₂₁, U₂₂ and U₂ represent the expected benefits of the building materials enterprise’s E₁ strategy, E₂ strategy and average expected benefit, respectively; let U₃₁, U₃₂ and U₃ represent the expected benefits of the university’s Q₁ strategy, Q₂ strategy and average expected benefit, respectively; and let U₄₁, U₄₂ and U₄ represent the expected benefits of the consumer’s S₁ strategy, S₂ strategy and average expected benefit, respectively. The expected benefits to the government, building materials enterprises, universities and consumers under the given probability are obtained, as shown in

Table 5. The expected payoffs for the government, building material enterprises, universities, and consumers under a given probability.

Subject	Expected Payoff
Government	U11 = xyz(K2 + J + H − βG1 − γG − G3) + x(1 − y)z(λU + J + H − γG − G3 − W3 − W4) + xy(1 − z)(K2 + H − βG1 − G3) + x(1 − y)(1 − z)(λU + H − G3 − W3 − W4) +(1 − x)yz(μU + J − αG1 − γG − W1) +(1 − x)y(1 − z)(μU − αG1 − W1) + (1 − x)(1 − y)z(μU + J − αG1 − γG − W1) + (1 − x)(1 − y)(1 − z)(μU − αG1 − W1)
	U12 = xyz(K2 + J + T − Z) + x(1 − y)z(J + T − Z) + xy(1 − z)(K2 + T − Z) + x(1 − y)(1 − z)(T − Z) + (1 − x)yz(J + T − Z) + (1 − x)y(1 − z)(T − Z) + (1 − x)(1 − y)z(J + T − Z) + (1 − x)(1 − y)(1 − z)(T − Z)
	U1 = pU11 + (1 − p)U12
BMEs	U21 = pyz(L1 + K1 + O1 − F − C1 − M) + p(1 − y)z(L1 + F + O1 − F − C1 − M) + py(1 − z)(L1 + K1 + O1 − F − C1 − M) + p(1 − y)(1 − z)(L1 + F + O1 − F − C1 − M) + (1 − p)yz(L1 + K1 + O1 − F − C1 − M) + (1 − p)y(1 − z)(L1 + K1 + O1 − F − C1 − M) + (1 − p)(1 − y)z(L1 + F + O1 − F − C1 − M) + (1 − p)(1 − y)(1 − z)(L1 + F + O1 − F − C1 − M)
	U22 = pyz(αG1 + L2 − C2 − μU) + p(1 − y)z(αG1 + L2 − C2 − μU) + py(1 − z)(αG1 + L2 − C2 − μU) + p(1 − y)(1 − z)(αG1 + L2 − C2 − μU) + (1 − p)yz(L2 − C2) + (1 − p)y(1 − z)(L2 − C2) + (1 − p)(1 − y)z(L2 − C2) + (1 − p)(1 − y)(1 − z)(L2 − C2)
	U2 = xU21 + (1 − x)U22
Universities	U31 = pxz(βG1 + F + M + K3 − C3) + p(1 − x)z( − C3) + px(1 − z)(βG1 + F + M + K3 − C3) + p(1 − x)(1 − z)(−C3) + (1 − p)xz(K3 + F + M − C3) + (1 − p)x(1 − z)(K3 + F + M − C3) + (1 − p)(1 − x)z(−C3) + (1 − p)(1 − x)(1 − z)(−C3)
	U32 = pxz(F + M + O2 − λU − W2 − C4 − F) + p(1 − x)z(−C4) + px(1 − z)(−C4) + p(1 − x)(1 − z)(−C4) + (1 − p)xz(O2 + F + M − W2 − C4 − F) + (1 − p)x(1 − z)(O2 + F + M − W2 − C4 − F) + (1 − p)(1 − x)z(−C4) + (1 − p)(1 − x)(1 − z) (−C4)
	U3 = yU31 + (1 − y)U32
Consumers	U41 = pxy(γG + R1 − C5 − θ) + p(1 − x)y(γG + R1 − C5 − θ) + px(1 − y)(γG + R1 − C5 − θ − W4) + p(1 − x)(1 − y)(γG + R1 − C5 − θ) + (1 − p)x(1 − y)(R1 − C5 − θ − W4) + (1 − p)(1 − x)y(R1 − C5 − θ) + (1 − p)(1 − x)(1 − y)(R1 − C5 − θ)
	U42 = pxy(R2 − C5) + p(1 − x)y(R2 − C5) + px(1 − y)(R2 − C5) + p(1 − x)(1 − y)(R2 − C5) + (1 − p)xy(R2 − C5) + (1 − p)x(1 − y)(R2 − C5) + (1 − p)(1 − x)y(R2 − C5) + (1 − p)(1 − x)(1 − y)(R2 − C5)
	U4 = zU41 + (1 − z)U42

.

To consider the long-term game behavior and strategy selection of the government, BMEs, universities and consumers, a time factor is introduced, and the replicator differential dynamic equations of the four-party evolutionary game can be listed as follows:

$$\left\{\begin{array}{l}F(p)={\displaystyle \frac{dp}{dt}}=G(p)= p(U_{11}-U_1) =p(1-p) (T-Z+\alpha G_1+x(G_3+W_3+W_4-\alpha G_1-\lambda U-\mu U)+\mathrm{z}\gamma G_2\\ +xy(\lambda U+\mu U-W_3-W_4+\beta G_1))\\ F(x)={\displaystyle \frac{dx}{dt}}=E(x)= x(U_{21}-U_2) =x(1-x) (C_1-C_2-F-L_1+L_2+M+W_1-O_1+F+p(\alpha G_1+2O_1-\mu U)\\ +y(\mu U+F-K_1-W_1)-2py{O}_1-2pz{O}_1+2pyz{O}_1) \\ F(y)={\displaystyle \frac{dy}{dt}}= Q(\mathrm{y})= y(U_{31}-U_3) =-y(1-y) (C_4-C_3+x(F+K_3-O_2+W_2) +px(\beta G_1+\lambda U) ) \\ F(z)={\displaystyle \frac{dz}{dt}}= S(z)= z(U_{41}-U_4) =-z(1-z) (R_1-R_2-\theta +p\gamma G_2-x{W}_4+xy{W}_4) \end{array}\right.$$

(1)

4. Asymptotic Stability Analysis of the Strategies of Four-Party Game Entities

According to the stability theorem of the replicator dynamic equation, it can be known that $F(p)=0$ and $F\prime (p)<0$ when $F\left(x\right)=0$ and $F^{\prime }\left(x\right)<0$; $F\left(y\right)=0$ and $F^{\prime }\left(y\right)<0$; $F\left(z\right)=0$ and $F^{\prime }\left(z\right)<0$; and $p*$, $x*$, $y*$, $z*$, the stable strategies, respectively, representing the government, BMEs, universities and consumers in the evolution.

4.1. The Asymptotic Stability Analysis of the Government’s Strategic Behaviors

From the replication dynamic equation, it can be known that:

$$\begin{array}{l}{F}^{\prime }\left(p\right)=(1-2p\left)\right(T-\mathrm{Z}+\alpha G_1+x(G_3+W_3+W_4-\alpha G_1-\lambda U-\mu U)+z\gamma G_2+\\ xy(\lambda U+\mu U-W_3-W_4+\beta G_1\left)\right)\end{array}$$

(2)

Let $T-Z+\alpha G_1+x(G_3+W_3+W_4-\alpha G_1-\lambda U-\mu U)+z\gamma G_2+xy(\lambda U+\mu U-W_3-W_4+\beta G_1)$, $G(z)=0$ Solving gives $z=z*={\displaystyle \frac{T-\mathrm{Z}+\alpha G_1+x(G_3+W_3+W_4-\alpha G_1-\lambda U-\mu U)+xy(\lambda U+\mu U-W_3-W_4+\beta G_1)}{-\gamma G_2}}$ In this situation, the government’s choice of either a “strict regulation” or a “lenient regulation” will not alter the outcome, meaning that the ratio of strategies remains constant over and serves as the dividing line of stable state $G\left(z\right)\ne 0$, $G(z)=0$. Differentiating w.r.t. z, we have $dG(z)/dz=\gamma G_2>0$, $G\left(z\right)$, which is a function that increases with respect to z,z > z*, $G(z)>0$, as shown in Figure 2a. At this point, $F^{\prime }(0)>0$, $F^{\prime }(1)<0$, in this case, z = 1. It is the system’s evolutionarily stable strategy. Specifically, the government opts for the “lax supervision”. z = 0. It is in an unstable state, that is, the government selects the “strict regulation”. As the evolution progresses, the government eventually evolves towards the direction of choosing the “lenient regulation”, as shown in Figure 2b. z < z*, $G(z)>0$. $F^{\prime }(0)<0$, $F^{\prime }(1)>0$, In this case, z = 0. It is the system’s evolutionarily stable strategy. The government chooses the “strict regulation”, z = 1. This is an unstable state, that is, the government selects the “loose regulation”. As the evolution deepens, the government gradually shifts toward choosing the “strict regulation”, as shown in Figure 2c. It should be noted that z* represents the critical probability of consumers’ DG purchasing behavior, which essentially reflects the balance point between “market demand signals” and “government regulatory costs”. When the probability of consumers’ DG purchasing z is greater than z*, the spontaneous green demand in the market can already drive enterprises to transform. The benefits of the government’s lenient regulation (such as tax growth and reduction in credibility maintenance costs) are greater than the administrative costs of strict regulation. The policy naturally evolves towards “less regulation, more service and facilitation”. When z is less than z*, the market demand is insufficient. It is necessary to make up for the “market failure” through strict regulation and force the industry chain to transform. The policy leverage can be precisely exerted. On one hand, by increasing consumer subsidies γ and strengthening the promotion of green products, z can be directly enhanced, promoting the transition of the regulatory strategy from “strict” to “lenient”; on the other hand, through simplifying the certification process of DG products and reducing the cognitive cost of consumers, z* can be reduced, enabling the government to maintain effective regulation at a lower consumption demand with low costs.

4.2. Analysis of the Gradual Stability of the Strategic Behaviors of BMEs

From the replicator dynamics equation, it can be known that:

$$\begin{array}{l}F\prime (x)=(1-2x)(C_1-C_2-F-L_1+L_2+M+W_1-O_1+F+p(\alpha G_1+2O_1-\mu U)\\ +y(\mu U+F-K_1-W_1)-2py{O}_1-2pz{O}_1+2pyz{O}_1)\end{array}$$

(3)

When $\begin{array}{l}G(z)=C_1-C_2-F-L_1+L_2+M+W_1-O_1+F+p(\alpha G_1+2O_1-\mu U)\\ +y(\mu U+F-K_1-W_1)-2py{O}_1-2pz{O}_1+2pyz{O}_1)\end{array}$, $G\left(\mathrm{z}\right)=0$, $z=z^{**}={\displaystyle \frac{C_1-C_2-F-L_1+L_2+M+W_1-O_1+F+p(\alpha G_1+2O_1-\mu U)+\mathrm{y}(\mu U+F-K_1-W_1)+2pyz{O}_1) }{2p{O}_1-2py{O}_1 }}$. In this situation, whether building material enterprises choose the “active DG transformation” or “passive DG transformation”, it will not change the outcome, that is, the ratio of strategies remains constant overall. See Figure 3a. $G(z)\ne 0$, $G(z)$. Differentiating w.r.t. z, we have $dG(z)/dz=2p(y-1)O_1 <0$. Therefore, $G\left(z\right)$. It is a decreasing function with respect to z, so z > z**, $G(z)<0$. At this moment, $F^{\prime }(0)<0$, $F^{\prime }(1)>0$, z = 0. It is the evolutionarily stable strategy of the system. That is, when z = 0, the BMEs choose the “active DG transformation”, while when z = 1, it is an unstable state, that is, the BMEs choose the “passive DG transformation”. As the evolution deepens, the BMEs eventually evolve in the direction of choosing the “active DG transformation”, as shown in Figure 3b. z < z**, $G(z)>0$, at this moment, $F^{\prime }(0)>0$, $F^{\prime }(1)<0$, z = 1. It is the evolutionarily stable strategy of the system, that is, BMEs choose the “passive DG transformation”, and z = 0 is in an unstable state. That is, BMEs choose the “active DG transformation”. As the evolution deepens, BMEs eventually evolve in the direction of choosing the “passive DG transformation”, as shown in Figure 3c. It should be noted that z** represents the “cost–benefit” critical value for enterprises’ proactive DG transformation. The core aspect reflects the pulling effect of market demand on enterprises’ decisions. When the probability of consumers purchasing DG products, z, is greater than z**, the market premium of green products is sufficient to cover the transformation costs (such as R&D costs and equipment renewal costs C₁), and the net profit from the enterprises’ proactive transformation is positive. The strategy naturally converges towards “proactive transformation”; when z is less than z**, market demand is insufficient to support the transformation returns, and enterprises tend to choose the low-cost “passive transformation” to avoid risks. At the policy level, efforts can be made in two aspects: one is to expand the market scale of DG products through government centralized procurement and mandatory implementation of green building standards, directly raising z; the other is to reduce the marginal cost of transformation for enterprises through stepped subsidies α (increased subsidy ratio in the initial stage of transformation) and tax exemptions, thereby lowering z**, allowing enterprises to achieve transformation profits even during lower market demand.

4.3. A Progressive Stability Analysis of Strategic Behaviors in Higher Education Institutions

From the replication dynamic equation, it can be known that:

$$F\left(\mathrm{y}\right)=(2y-1) (C_4-C_3+x(F+K_3-O_2+W_2) +px(\beta G_1+\lambda U) )$$

(4)

Let $G\left(\mathrm{x}\right)= C_4-C_3+x(F+K_3-O_2+W_2) +px(\beta {\mathrm{G}}_1+\lambda U)$, $G\left(\mathrm{x}\right)=0$, so the solution is $x=x*={\displaystyle \frac{C_4-C_3+x(F+K_3-O_2+W_2)}{-p(\beta G_1+\lambda U)}}$. In this situation, the choice of either the “active DGS” or the “passive DGS” by universities will not alter the outcome. That is, the ratio of strategies remains constant overall, as shown in Figure 4a. $G\left(\mathrm{x}\right)\ne 0$, $\mathrm{G}\left(\mathrm{x}\right)$. Differentiating w.r.t. x, we have: ${\displaystyle \frac{dG(x)}{dx}}=p(\beta G_1+\lambda U)>0$; therefore, $\mathrm{G}\left(\mathrm{x}\right)$ is increasing with x, x > x*, G(x) > 0, at this moment, $F^{\prime }(0)<0$, $F^{\prime }(1)>0$, x = 0. It is the evolutionarily stable strategy of the system, that is, universities choose the “passive DGS”, while x = 1 is an unstable state, that is, universities choose “strict cooperation”. As the evolution progresses, universities eventually evolve towards a state where all choose the “passive DGS”, as shown in in Figure 4b. x < x*, G(x) < 0, at this moment, $F^{\prime }(0)>0$, $F^{\prime }(1)<0$, x = 1. It is the systemic evolutionarily stable strategy, in which universities choose the “active DGS”, while x = 0 is an unstable state, that is, universities choose the “passive DGS”. As the evolution deepens, universities eventually evolve towards a state where all choose the “active DGS”, as shown in Figure 4c. It should be noted that x* represents the “collaborative benefit” threshold for universities to actively participate in the DG transformation. It reflects the interactive relationship between the enterprise’s transformation initiative and the university’s innovation drive. When the probability of the enterprise’s active transformation x is greater than x*, the technological transformation benefits (such as joint R&D funds, shared f achievements and commercialization) from the cooperation between the university and the enterprise are insufficient to cover the basic research cost C₃. The university is inclined to choose “passive transformation”; when x is less than x*, the urgent need of the enterprise for core technologies drives a deep binding among industry–universities–research, and the comprehensive benefits (including government subsidies βG₁ and improvement of industry reputation) obtained by the universities through technology output and talent cultivation exceed the research cost. The strategy evolves towards “active transformation”. Policies can increase the direct benefits of universities’ active transformation by establishing special funds for industry–universities–research cooperation and incorporating the effectiveness of technology transformation into the university’s assessment system. At the same time, by reducing the transaction costs of cooperation between enterprises and universities (such as establishing a technology transfer platform), the positive transmission of x to the university’s strategy is strengthened, thereby reducing x*.

4.4. A Progressive Stability Analysis of Consumer Strategic Behavior

Let $G(y)=R_1-R_2-\theta +p\gamma G_2-x{W}_4+xy{W}_4$, $G(y)= 0$; therefore, the solution is $y=y*={\displaystyle \frac{R_1-R_2-\theta +p\gamma G_2-x{W}_4 }{-x{W}_4 }}$. In this situation, whether consumers choose the “DG purchase” or “traditional purchase”, the outcome will not change. That is, the ratio of strategies remains constant overall, as shown in Figure 5a. $G\left(y\right)\ne 0$. Differentiating $G\left(y\right)$ with respect to y, we have: ${\displaystyle \frac{dG(y)}{dy}}=x{W}_4>0$; therefore, $G\left(y\right)$ is increasing with y, so y > y*, G(y) > 0, $F^{\prime }(0)<0$, $F^{\prime }(1)>0$, y = 0. It is the evolutionarily stable strategy of the system, that is, consumers choose the “DG purchase”, while y = 1 is an unstable state, that is, consumers choose the “traditional purchase”. As the evolution progresses, consumers eventually evolve towards a state where all choose the “DG purchase”, as shown in Figure 5b. y < y*, G(y) < 0, $F^{\prime }(0)>0$, $F^{\prime }(1)<0$, y = 1. Consumers choose the “traditional purchase”. However, y = 0 represents an unstable state, meaning that consumers choose the “DG purchase”. As the evolution progresses, consumers eventually evolve towards a state where all choose the “traditional purchase”, as shown in Figure 5c. It should be noted that y* represents the “trust and value” threshold that consumers consider when choosing DG products. This core aspect reflects the supporting role of university technology empowerment in consumers’ decision-making. When the probability of university active transformation y > y*, the university’s technical endorsement (such as green technology certification, product environmental protection education) reduces the information asymmetry cost for consumers. The environmental value and digital service value (such as full life cycle traceability) of DG products are sufficient to cover the preference cost θ, and consumers tend to “purchase DG products”. When y < y*, consumers have doubts about the technical reliability and environmental authenticity of DG products and are more inclined to choose familiar traditional products. Policies can strengthen the university’s trust endorsement for consumers’ decision-making by supporting universities in conducting green technology education, establishing DG product traceability platforms (with technical support provided by universities), etc.; at the same time, through consumption subsidy γG₂, the purchase cost of DG products can be directly reduced, increasing the net benefit of consumers’ choice and thereby lowering y*.

In order to systematically analyze the gradual stability characteristics of the strategies of the four types of game participants, namely, the government, BMEs, universities, and consumers, and to clearly present the core logic of each participant’s strategy choices, the evolutionary stable states, key influencing factors, and dynamic evolution patterns, the abovementioned core research results are summarized as shown in

Table 6. The summary of asymptotic stability analysis results of four-party game participants’ strategies.

Game Participants	Core Conclusions of Replicator Dynamics	Evolutionarily Stable Strategy (ESS)	Key Influencing Factors	Evolutionary Characteristics
Government	Strategy choice depends on consumers’ DG purchase probability z, which tends to lenient regulation when z > z∗ and strict regulation when z < z∗	z = 1 (lenient regulation) or z = 0 (strict regulation)	Consumers’ DG purchase probability (z)	Dynamically adjusts with consumer behavior, no fixed initial strategy, and ultimately converges to a single regulatory model
Building Materials Enterprises (BMEs)	Strategy choice is negatively correlated with consumers’ DG purchase probability z, selecting active transformation when z > z∗∗ and passive transformation when z < z∗∗	z = 0 (active DG transformation) or z = 1 (passive DG transformation)	Consumers’ DG purchase probability (z)	Sensitive to market feedback; the stronger consumers’ green demand, the higher enterprises’ willingness to adopt active transformation
Universities	Strategy choice is positively correlated with enterprises’ active transformation probability x, selecting passive transformation when x > x∗ and active transformation when x < x∗	x = 1 (active DG transformation) or x = 0 (passive DG transformation)	Enterprises’ active transformation probability (x)	Relies on feedback from enterprises’ transformation behavior; the higher enterprises’ active participation, the stronger universities’ willingness to engage in collaborative innovation
Consumers	Strategy choice is positively correlated with universities’ active transformation probability y, selectin DG purchase when y > y∗ and traditional purchase when y < y∗	y = 0 (DG purchase) or y = 1 (traditional purchase)	Universities’ active transformation probability (y)	Influenced by universities’ technological empowerment and product promotion; the more sufficient universities’ active transformation, the stronger consumers’ willingness to make green purchases

.

5. Stability Analysis of Strategy Combinations in the Four-Party Game

Based on the Lyapunov stability theory, to determine the evolutionary direction and the final evolutionarily stable strategies (ESSs) of each party, it is necessary to conduct a stability analysis. Through examining the local stability of the Jacobian matrix associated with the replicator dynamic equations, the equilibrium evolutionary stability of the system can be determined.

Based on the four-party replicator dynamic equations derived in Equation (1), the Jacobian matrix J of the system is calculated as follows:

$$J=\left[\begin{array}{cccc}{\displaystyle \raisebox{1ex}{$\partial F\left(p\right)$}\!\left/ \!\raisebox{-1ex}{$\partial p$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(p\right)$}\!\left/ \!\raisebox{-1ex}{$\partial x$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(p\right)$}\!\left/ \!\raisebox{-1ex}{$\partial y$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(p\right)$}\!\left/ \!\raisebox{-1ex}{$\partial z$}\right.}\\ {\displaystyle \raisebox{1ex}{$\partial F\left(x\right)$}\!\left/ \!\raisebox{-1ex}{$\partial p$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(x\right)$}\!\left/ \!\raisebox{-1ex}{$\partial x$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(x\right)$}\!\left/ \!\raisebox{-1ex}{$\partial y$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(x\right)$}\!\left/ \!\raisebox{-1ex}{$\partial z$}\right.}\\ {\displaystyle \raisebox{1ex}{$\partial F\left(y\right)$}\!\left/ \!\raisebox{-1ex}{$\partial p$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(y\right)$}\!\left/ \!\raisebox{-1ex}{$\partial x$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(y\right)$}\!\left/ \!\raisebox{-1ex}{$\partial y$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(y\right)$}\!\left/ \!\raisebox{-1ex}{$\partial z$}\right.}\\ {\displaystyle \raisebox{1ex}{$\partial F\left(z\right)$}\!\left/ \!\raisebox{-1ex}{$\partial p$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(z\right)$}\!\left/ \!\raisebox{-1ex}{$\partial x$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(z\right)$}\!\left/ \!\raisebox{-1ex}{$\partial y$}\right.}& {\displaystyle \raisebox{1ex}{$\partial F\left(z\right)$}\!\left/ \!\raisebox{-1ex}{$\partial z$}\right.}\end{array}\right]$$

(5)

In multi-population evolutionary games, the condition for an evolutionarily stable strategy must be a strict Nash equilibrium [54], and this strict Nash equilibrium is a pure strategy [55]. Therefore, in the replicative dynamic system composed of the government, BMEs, universities and consumers, let $F(p)=F(x)=F(y)=F(z)=0$, and let $R=\{(p,x,y,z)|0\le p\le 1,0\le x\le 1,0\le y\le 1,0\le z\le 1\}$. The following conclusions can be drawn: ① There must exist 16 equilibrium points where the four parties adopt pure strategies, respectively: $E_1(0,0,0,0)$, $E_2(0,0,0,1)$, $E_3(0,0,1,0)$, $E_4(0,0,1,1)$, $E_5(0,1,0,0)$, $E_6(0,1,0,1)$, $E_7(0,1,1,0)$, $E_8(0,1,1,1)$, $E_9(1,0,0,0)$, $E_{10}(1,0,0,1)$, $E_{11}(1,0,1,0)$, $E_{12}(1,0,1,1)$, $E_{13}(1,1,0,0)$, $E_{14}(1,1,0,1)$, $E_{15}(1,1,1,0)$, $E_{16}(1,1,1,1)$. ② There may exist one mixed strategy equilibrium point. $E_{17}(p*,x*,y*,z*)$ and $p*,x*,y*,z*\in (0,1)$. Appendix A is the Proof of the stability of evolutionary stable strategy.

(1)

Stability analysis of strategy combinations under lenient government regulation.

An analysis of the asymptotic stability of the equilibrium points of the replicator dynamic system is presented in

Table 7. Stability analysis of the equilibrium point under lenient government regulation.

Equilibrium Point	Eigenvalue				Sign	Stability
	λ1	λ2	λ3	λ4
(1, 0, 0, 0)	C4 − C3	T − Z + αG1	R2 − R1 − γG2 + θ	C2 − C1 + K1 + L1 − L2 − M + O1 − F − αG1	− + x +	Unstable
(1, 0, 0, 1)	C4 − C3	R2 − R1 − γG2 + θ	G2 + T − Z + αG1	C2 − C1 + K1 + L1 − L2 − M + O1 − F − αG1	− x + +	Unstable
(1, 0, 1, 0)	C3 − C4	T − Z + αG1	γG2 + R1 − R2 − θ	C2 − C1 + K1 + L1 − L2 − M + O1 − F − αG1	+ + x +	Unstable
(1, 0, 1, 1)	C3 − C4	R2 − R1 − γG2 + θ	γG2 + T − Z + αG1	C2 − C1 + K1 + L1 − L2 − M + O1 − F − αG1	− x + +	Unstable
(1, 1, 0, 0)	γG2 + R1 − R2 − W4 − θ	T − G3 − μU − W1 − W3 − λU − Z	C4 − C3 + F − K3 − O2 + W2 + λU − βG1	C1 − C2 − L1 + L2 + M + W1 − O1 + αG1	− − − −	ESS
(1, 1, 0, 1)	R2 − R1 − G2 + W4 + θ	γG2 + G3 + T − Z − λU − μU	C4 − C3 + F + K3 − O2 + W2 + λU + βG1	C1 − C2 − F − L1 + L2 + M + W1 − O1 + F + αG1	+ + − −	Unstable
(1, 1, 1, 0)	γG2 + R1 − R2 − θ	G3 + T − Z + βG1	C3 − C4 − F − K3 + O2 − W2 − λU − βG1	C1 − C2 − K1 − L1 + L2 + M − O1 + F + αG1	x + + −	Unstable
(1, 1, 1, 1)	R2 − R1 − γG2 + θ	G2 + G3 + T − Z + βG1	C3 − C4 − F − K3 + O2 − W2 − λU − βG1	C1 − C2 − K1 − L1 + L2 + M − O1 + F + αG1	x + + −	Unstable

Note: x indicates that the sign of the eigenvalue of the Jacobian matrix is undetermined; + indicates that the eigenvalue of the Jacobian matrix is greater than 0; and − indicates that the eigenvalue of the Jacobian matrix is less than 0; the same is shown below.

for the case when the government’s stability strategy is passive regulation, that is, when the conditions are met: $T-Z+\alpha X_1+x\left(G_3+W_3+W_4-\alpha G_1-\lambda U)+z{G}_2+xy\right(\lambda U-W_3-W_4+\beta G_1)>0$. As can be seen from Table 7, there is only one evolutionarily stable point in the evolutionary game among the four participating entities, which is (1, 1, 0, 0). For instance, a certain province did not introduce a mandatory DG transformation policy (the government chose option G₂: lenient regulation), merely maintaining normal tax collection and management without any special subsidies (α = 0, β = 0) or strict environmental protection inspections. A local cement enterprise planned to undergo DG transformation and collaborated with a certain building materials college (a university). Consumers still mainly purchased traditional building materials. The corresponding evolutionary strategy is (strict government regulation, proactive digital and green transformation of building material enterprises, passive digital and green transformation of universities, and traditional purchasing by consumers) [56]. It simultaneously meets conditions ①–④. Condition ① is R₂ < [(R₁ + γG₂) − (W₄ + θ)], that is, the benefit of consumers’ traditional purchases is less than the difference between the sum of the benefit of consumers’ DG purchases and the government’s DG consumption subsidies for consumers and the sum of consumers’ DG purchases and the loss of consumer experience when universities undergo a “passive DGS”. This condition clearly defines the “net benefit threshold” for consumers choosing to purchase DG products—the traditional purchase benefit must be lower than the “total net benefit” of DG purchases (including product value and government subsidies) minus the experience loss brought about by the universities’ passive transformation. Its essence is the balance between the consumers’ “green consumption intention” and “actual cost”: when the combined value of DG products (environmental protection + digital services) plus subsidies is sufficient to cover the preference cost and experience loss, consumers will abandon traditional purchases. The policy can directly increase the benefit end of DG purchases by raising the consumption subsidy γG₂ or it can promote universities to standardize technology output, reduce passive transformation behaviors (lower W₄), and simplify the purchase process of DG products (lower θ) simultaneously, thus reducing this threshold and making the condition easier to meet. Condition ② is T − Z < (G₃ + W₁ + W₃ + λU + μU), that is, the difference between the normal tax revenue and the loss of credibility when the government implements “lenient supervision” is less than the sum of the regulatory costs when the government actively promotes the digital and green transformation of BMEs and universities, the additional regulatory costs when the government passively supervises the digital and green transformation of BMEs and universities, and the transition adaptation regulatory payments collected. This condition defines the “cost–benefit boundary” of the government’s regulatory strategy—the net benefit of lenient regulation (tax T minus credibility loss Z) must be lower than the total benefit of strict regulation (including active regulatory costs G₃, additional regulatory costs for passive transformation W₁ + W₃, and fine income λU + μU). The core is that the government needs to compensate for the regulatory costs through a “punishment mechanism”: when the fine income from the passive transformation of enterprises and universities is high enough and the additional regulatory costs are controllable, strict regulation becomes more economically viable. The policy can adjust the intensity of transition adaptation regulation parameters λ and μ (linked to the transformation stage) to ensure that the fine income can cover the regulatory costs; at the same time, it can optimize the regulatory process (such as digital regulatory means) to reduce costs such as G₃ and W₁ and enhance the satisfaction of this condition. Condition ③ is C₄ + F + W₂ + λU < C₃ + K₃ + O₂ + βG₁. When the sum of the costs of a university’s “passive DGS”, the loss of market trust, the penalty paid to building material enterprises for breach of contract, and the transition adaptation regulation fees paid to the government is less than the sum of the costs of the university’s “active DGS”, the government’s DG investment subsidies obtained by the university through “active DGS”, the spillover benefits generated by the university due to the knowledge input of building material enterprises, and the trust benefits gained by the university through “active DGS”, the university will choose passive DGS” [57]. This condition reflects the “benefit–cost balance” of the proactive transformation of universities—the total cost of passive transformation (operational cost C₄, penalty for default F, loss of market trust W₂, transition adaptation regulatory penalty λU) must be lower than the total benefit of proactive transformation (research and development cost C₃, trust benefit K₃, technology spillover benefit O₂, government subsidy βG₁). Its essence is to motivate universities to shift from “passive compliance” to “active innovation”. Policies can enhance the benefit side of proactive transformation by increasing the subsidy β for proactive transformation of universities and incorporating the technology spillover benefit into the university incentive system. At the same time, by strictly implementing the penalty F as the default, strengthening the reputation management of universities (increasing W₂), and increasing the opportunity cost of passive transformation, the condition can be fulfilled. Condition ④ is (L₂ − C₂ + αG₁) < (L₁ − C₁ − M + O₁), that is, the sum of the market gains obtained by the BME through passive DGS and the government subsidies for the DG investment of the BME minus the DG costs incurred by the BME during passive DGS is less than the sum of the market gains obtained by the BME through active DGS and the spillover benefits generated by the BME due to the knowledge input of universities for “passive DGS” minus the sum of the market gains obtained by the BME through active DGS, the DG costs of active DGS of the BME and the DG service fees paid by the BME to the university [58]. This condition clearly defines the “profit threshold” for enterprises to undertake proactive transformation—the net income from passive transformation (market revenue L₂ plus government subsidies αG₁ minus transformation cost C₂) must be lower than the net income from proactive transformation (market revenue L₁, technology spillover revenue O₁ minus transformation cost C₁, and service fee M). The core idea is to use both market and policy incentives to ensure that the long-term benefits of enterprises’ proactive transformation exceed the short-term speculative benefits. Policies can enhance the benefits of proactive transformation by increasing the subsidy α for proactive transformation, expanding the market demand for DG products (pushing up L₁), etc.; at the same time, by strengthening environmental supervision (increasing the implicit costs of passive transformation, such as reputation loss), reducing the service fee M for cooperation between enterprises and universities, and narrowing the profit space for passive transformation, we can ensure that the conditions will be met.

This paper quantified the above core parameters based on real industry scenarios. In terms of enterprise transformation costs, C₁ (active transformation cost) refers to the 10-billion-yuan-level transformation fund support standards in the building materials industry of provinces such as Zhejiang and Anhui combined with the actual investment of a leading cement enterprise in a certain region (such as Group A), including 120 million yuan for digital kiln monitoring systems, 100 million yuan for carbon capture equipment, and 30 million yuan for compatible technological transformation, totaling 250 million yuan, which conforms to the model’s “C₁ > C₂” setting. C₂ (passive transformation cost) is based on the basic environmental protection compliance requirements of the “Environmental Protection Law”, requiring only 80 million yuan for bottom-line equipment, such as desulfurization and dust removal, and 20 million yuan for a small amount of compliance testing costs, totaling 100 million yuan, forming a reasonable gradient with the active transformation cost. In terms of university research and development investment, C₃ (active transformation cost) refers to the construction standards of scientific and technical research platforms in engineering colleges, with an annual investment of 120 million yuan, covering the establishment of a DG technology research and development team of 50 million yuan, the construction of a green building materials experimental platform of 40 million yuan, and long-term data collection and analysis of 30 million yuan, matching the model’s “C₃ > C₄” logic. C₄ (passive transformation cost) is based on the mature service technology model of universities, requiring only 30 million yuan for the maintenance of existing energy-saving calculation software and 20 million yuan for basic technical consulting personnel costs, totaling 50 million yuan, which conforms to the “only output existing technology” cost characteristic. In the government supervision and subsidy parameters, G₁ (special research and development fund) refers to the 20% equipment subsidy policy for intelligent factories in Inner Mongolia and the 20% revenue subsidy policy for DG consulting services of universities in Wenjiang District, Chengdu, with α = 0.2 and β = 0.2; therefore, G₁ = 1 billion yuan (the scale of provincial typical transformation fund). G₃ (strict supervision cost) combines the operation costs of local environmental protection inspection teams of 30 million yuan, the construction of digital supervision platforms of 30 million yuan, and cross-departmental coordination costs of 20 million yuan, totaling 80 million yuan, conforming to the actual supervision investment structure. In the consumer-related parameters, θ (green preference cost) is based on the DG product detection cost of real estate developers of 0.15 billion yuan per project and the training cost for project and construction process adaptation of 0.05 billion yuan, totaling 0.2 billion yuan, reflecting the additional cost caused by information asymmetry. C₅ (traditional procurement cost) refers to the average purchase price of building materials in the industry, with the total cost of ordinary cement purchase + transportation + storage of 4 billion yuan per project and that of DG cement, due to the certification premium, increasing by 0.3 billion yuan, consistent with the model’s “lower traditional procurement cost”.

For enterprises, the net benefit of taking the initiative to transform is significantly higher than that of undergoing a passive transformation. Group A won two key engineering orders through the optimization of digital kilns and the certification of low-carbon cement, achieving a market revenue (L₁) of 400 million yuan. Its initiative transformation cost (C₁) was 250 million yuan, which included the investment in digital monitoring systems and carbon capture equipment, as well as the payment of 30 million yuan for the mature energy-saving technical services from universities. It also gained a technology spillover benefit (O₁) of 20 million yuan through the optimization of raw material ratios by drawing on university technology. If choosing a passive transformation, it could only have maintained the basic production capacity, with a market revenue (L₂) of 280 million yuan. The passive transformation cost (C₂) was 100 million yuan (only meeting the environmental protection bottom line of desulfurization equipment), and there were no special government subsidies (αG₁ = 0) under the relaxed supervision. During actual operation, Group A’s annual net profit increased from 80 million yuan to 140 million yuan after the initiative transformation. In contrast, small and medium-sized cement enterprises that chose passive transformation lost high-end orders and faced an average annual environmental penalty of 20 million yuan, resulting in a net profit of less than 30 million yuan. Eventually, 80% of regional leading enterprises chose the initiative transformation, which was in line with the “enterprise initiative” requirement of ESSs.

For universities, the total cost of passive transformation is lower than that of initiative transformation. B Polytechnic University only needed to provide mature energy-saving calculation software for passive transformation, without any cutting-edge research and development investment. The cost (C₄) was 50 million yuan. Due to only signing basic technical service contracts without any research and development commitments, the breach of contract compensation (F) was 0, and there were no major technical accidents, so the university only faced a minor reputation loss (W₂) of 10 million yuan under relaxed supervision. However, if choosing initiative transformation, the costs of establishing a DG technical research and development team and building an experimental platform (C₃) would have been as high as 120 million yuan. Even if the university could obtain a trust benefit of 30 million yuan from a few enterprise cooperation intentions and 10 million yuan of knowledge spillover from the assistance of enterprise production data in research, and without any government research and development subsidies (βG₁ = 0), it would have taken 5 years to recover the cost. In contrast, providing mature technology through passive means had an average annual revenue of 20 million yuan, with a higher input–output ratio. Therefore, B Polytechnic University ultimately chose “only outputting existing technology”, which was in line with the “university passive” feature of ESSs.

For consumers, the net benefit of traditional purchases is higher than that of DG purchases. A real estate developer purchasing ordinary cement (traditional purchase), with low engineering costs and stable quality, could obtain a 300 million yuan benefit (R₂). If the develop chose a DG purchase, the environmental protection value of low-carbon cement and the digital traceability service could have brought a 320 million yuan benefit (R₁), but the government had no relevant consumption subsidies (γG₂ = 0), and DG cement required additional adaptation of construction processes, resulting in a 30 million yuan experience loss (W₄). The developer’s trust in the low-carbon certification was insufficient, and the developer would also have needed to bear an additional 20 million yuan detection cost (θ). In actual decision-making, the comprehensive cost of purchasing DG cement was 0.3 billion yuan higher per project than traditional cement, and due to concerns about technical adaptation risks, 90% of developers’ projects chose traditional cement, which was in line with the “consumer traditional purchase” ESS result.

For the government, the net loss under relaxed supervision is lower than the cost of strict supervision. Under relaxed supervision, the government could obtain 120 million yuan of industry annual tax revenue (T), and there was only a 30 million yuan loss in credibility (Z) due to a small number of environmental complaints. The net benefit was 90 million yuan. However, if strict supervision is implemented, the costs for establishing a special supervision team and building a digital supervision platform amount to 0.8 billion yuan (G₃), while the supervision costs for enterprises’ passive transformation (W₁) are 0.2 billion yuan, and the supervision costs for universities (W₃) are 0.1 billion yuan. Only by imposing a fine of 0.1 billion yuan for minor over-standard emissions from two enterprises (λU + μU) can a revenue of 0.1 billion yuan be obtained. The net profit is −1.0 billion yuan. Therefore, the government maintains a lenient supervision policy while using basic environmental protection standards to force enterprises not to abandon the transformation, forming the premise of “government relaxation but effective constraint” for the ESS.

In conclusion, in a relaxed regulatory environment, enterprises actively transform due to the disparity in market returns, universities passively provide technical services because the cost-effectiveness of their research is low, consumers prefer traditional purchases due to cost pressure and risk concerns, and the government maintains a relaxed stance due to the balance between regulatory costs and benefits. The strategies of the four parties are mutually compatible: the active transformation of enterprises meets the government’s environmental protection bottom-line requirements, the passive technology output of universities reduces the threshold for enterprise transformation, and the traditional demands of consumers do not require excessive investment by enterprises. Eventually, a stable equilibrium of ESS (1, 1, 0, 0) is formed, which is fully consistent with the conclusion of the model that “the stability of strategy combinations depends on the balance of interests”.

(2)

Analysis of the stability of strategy combinations under strict government regulation.

An analysis of the asymptotic stability of the equilibrium points of the replicator dynamic system is presented in

Table 8. Stability analysis of the equilibrium point under strict government regulation.

Equilibrium Point	Eigenvalue				Sign	Stability
	λ1	λ2	λ3	λ4
(0, 0, 0, 0)	C4 − C3	R1 − R2 − θ	Z − T − αG1	C2 − C1 + K1 + L1 − L2 − M + O1 − F	− − − +	Unstable
(0, 0, 0, 1)	C4 − C3	R2 − R1 + θ	Z − T − γG2 − αG1	C2 − C1 + K1 + L1 − L2 − M + O1 − F	− + − +	Unstable
(0, 0, 1, 0)	C3 − C4	R1 − R2 − θ	Z − T − αG1	C2 − C1 + K1 + L1 − L2 − M + O1 − F	− + + −	Unstable
(0, 0, 1, 1)	C3 − C4	R2 − R1 + θ	Z − T − γG2 − αG1	C2 − C1 + K1 + L1 − L2 − M + O1 − F	+ + − +	Unstable
(0, 1, 0, 0)	R1 − R2 − W4 − θ	Z − T − W3 − W4 − G3 + λU	C4 − C3 + F + K3 − O2 + W2	C1 − C2 − F − L1 + L2 + M+W1 − O1 + F	− x + −	Unstable
(0, 1, 0, 1)	R2 − R1 + W4 + θ	Z − G3 − T − W3 − W4 − γG2 + λU	C4 − C3 + F + K3 − O2 + W2	C1 − C2 − F − L1 + L2 + M+W1 − O1 + F	+ x + −	Unstable
(0, 1, 1, 0)	R1 − R2 − θ	Z − T − G3 − βG1	C3 − C4 − F − K3 + O2 − W2	C1 − C2 − K1 − L1 + L2 + M − O1 + F	− − − −	ESS
(0, 1, 1, 1)	R2 − R1 + θ	Z − T − G3 − βG1	C3 − C4 − F − K3 + O2 − W2	C1 − C2 − K1 − L1 + L2 + M − O1 + F	+ − − −	Unstable

for the case when the government’s stability strategy is strict regulation, that is, when the condition $T-Z+\alpha X_1+x\left(G_3+W_3+W_4-\alpha G_1-\lambda U)+z{G}_2+xy\right(\lambda U-W_3-W_4+\beta G_1)<0$ is met. From Table 8, it can be seen that there is only one evolutionary stable point in the evolutionary game among the four participating entities, which is (0, 1, 1, 0) [59]. The corresponding evolutionary strategy is (government lenient regulation, BMEs actively choosing digital and green transformation, universities actively choosing digital and green transformation, consumers choosing traditional purchasing), that is, simultaneously meeting conditions ⑤–⑧.

Condition ⑤ is R₁ − θ < R₂, that is, the difference between the benefits of consumers’ DG purchases and their preference for DG purchases is less than the benefits of consumers’ traditional purchases. This condition reflects the “value perception boundary” of consumers’ choices—the net gain from DG’s purchase (product value R₁ minus preference cost θ) needs to be lower than the traditional purchase benefit R₂. At this point, consumers still tend to make traditional purchases. The essence is that in the early stage of transformation, the market demand has not been fully cultivated, and it needs to be gradually guided through policies. Policies can reduce the preference cost θ of consumers (such as enhancing their awareness of DG products) through means like university science popularization and product experience activities; at the same time, through technological iterations, DG products can be upgraded to increase R₁ (such as optimizing the digital service experience), laying the foundation for the subsequent evolution of consumers’ strategies towards “DG purchase”. Condition ⑥ is (Z − T) < (G₃ + βG₁). The difference between the loss of government credibility during “lenient regulation” and the normal tax revenue is less than the regulatory cost of the government for the active DGS of BMEs and universities, as well as the DG subsidies provided by the government to universities [60]. This condition defines the “reasonable boundary” of the government’s lenient regulation—the net loss from lenient regulation (loss of credibility Z minus tax T) must be lower than the core cost of strict regulation (active transformation regulatory cost G₃, university subsidy βG₁). The core idea is that when market entities (enterprises, universities) have sufficient motivation to transform, the government can reduce the regulatory intensity while maintaining system stability at a lower administrative cost. The policy can reduce βG₁ by optimizing the subsidy structure (such as changing one-time subsidies to those based on transformation results) and reduce G₃ through digital regulatory means, thereby expanding the application scenarios of lenient regulation. Condition ⑦ is (C₃ + O₂ − K₃) < (C₄ + F+W₂), that is, the sum of the cost of the university’s active DGS and the spillover benefits generated by the knowledge input of building material enterprises is less than the sum of the cost of the university’s passive DGS, reputation loss, and penalty paid to building material enterprises. This condition clearly defines the “cost constraint” for the passive transformation of universities—the net cost of active transformation (research and development cost C₃ plus technology spillover benefit O₂ minus trust benefit K₃) must be higher than the overall cost of passive transformation (operating cost C₄, penalty for default F, and reputation loss W₂). At this point, universities are more inclined to undergo active transformation. The essence is to strengthen the cost constraint for passive transformation, thereby forcing universities to actively participate in innovation. Policies can increase the cost of passive transformation by raising the penalty for default F, improving the reputation evaluation system of universities (increasing W₂), etc. At the same time, by building a technology transfer platform, K₃ can be increased and the net cost of active transformation can be reduced, promoting the establishment of the conditions. Condition ⑧ is (L₂ − C₂) < (L₁ + O₁ + K₁ − C₁ − M − F), which shows the difference between the market gains obtained by the BME through passive DGS minus the DG costs during the passive DGS of the BME and the sum of the market gains obtained by the BME through active DGS, the spillover gains obtained by the BME through passive DGS and the value-added gains brought to the BME by the active DGS of the university minus the DG costs during the active DGS of the BME, and the sum of the DG service fees paid by the BME to the university and the penalty fees generated by the passive DGS of the BME [61]. This condition strengthens the “profit advantage” for enterprises to take the initiative in transformation—the net profit from passive transformation (market profit L₂—transformation cost C₂) must be lower than the comprehensive net profit from active transformation (market profit L₁, technological spillover benefit O₁, university empowerment value K₁—transformation cost C₁, service fee M, default fine F). The core idea is to enhance the comprehensive profit of enterprises taking the initiative in transformation through the collaboration of industry–universities–research while reducing the profit space for passive transformation. Policies can achieve this by supporting joint research and development between universities and enterprises (to increase K₁), establishing a transformation effectiveness reward fund (to increase L₁), etc., to amplify the profit advantage of active transformation; at the same time, by strictly enforcing the compensation for cooperative adjustments F, these policies ensure that passive transformation is unprofitable and encourage enterprises to adhere to the active transformation strategy in the long term.

According to the “Work Plan for Stabilizing Growth in the Building Materials Industry (2025–2026)”, the government implements strict supervision over the cement industry with the measures of “strictly prohibiting new production capacity + staged green subsidies”. On one hand, it strictly prohibits the addition of new cement clinker production capacity, requiring enterprises with excess capacity to complete capacity replacement by the end of 2025; on the other hand, for enterprises that actively carry out digital and green transformation (such as carbon capture, intelligent kilns), they will be given a 20% subsidy for equipment investment (α = 0.2), and at the same time, for enterprises with poor environmental performance, continuous daily penalties will be imposed (μU, U is 1 million yuan per instance). The main participants are local governments, regional cement enterprises (such as Southern Cement), building-materials-related universities (such as Wuhan University of Technology), and real estate developers (consumers).

The government chose “strict regulation”, investing 80 million yuan to establish a special supervision team (G₃) and set up a dynamic monitoring platform for cement production capacity. Using “capacity replacement review + environmental real-time monitoring” as dual constraints, it ensured the implementation of the policy. Although the regulatory cost was higher than the lenient model, it gained social benefits of H = 300 million yuan by eliminating inefficient production capacity (reducing annual carbon emissions by approximately 5 million tons), and the loss of credibility Z was nearly 0, which was in line with the model’s logic that “strict regulation yields higher net benefits than lenient regulation”.

Southern Cement chose “active DG transformation”, investing 600 million yuan (C₁) in building a digital carbon management system and carbon capture equipment, receiving a government subsidy of 120 million yuan (αG₁, G₁ = 600 million yuan) and at the same time obtaining three key project orders through low-carbon cement certification, with market revenue L₁ = 800 million yuan. Meanwhile, the small and medium-sized cement enterprises that chose passive transformation faced daily fines of 200,000 yuan (μU) due to non-compliance with environmental protection standards and were unable to participate in government project bidding, with market revenue L₂ = 200 million yuan. Eventually, 90% of the regional leaders chose active transformation, which met the “enterprise active” requirement of ESSs.

Wuhan University of Technology chose “active DG transformation”, establishing a DG technology research and development team (C₃ = 150 million yuan) and jointly building a “green cement joint laboratory” with Southern Cement, receiving a government research subsidy of 30 million yuan (βG₁, β = 0.2), and through technology transfer they obtained service revenue M = 50 million yuan. If they chose passive transformation (only outputting mature technology), they would have lost subsidies and long-term cooperation opportunities, and the knowledge spillover benefit O₂ would have been nearly 0. Therefore, the university had a strong desire for active transformation, which met the “university active” characteristic.

Real estate developers initially chose “traditional purchase” (R₂ = 3 billion yuan/project) due to the high cost of DG cement procurement (10% higher than traditional cement). However, as the government required government projects to use green building materials, and the universities reduced consumer trust costs θ (from 0.2 billion yuan to 0.05 billion yuan) through technology endorsement, starting from 2026, 30% of the projects began to choose DG procurement before gradually transitioning to “green purchase”, which conformed to the logic of the model that “consumer strategies evolve with regulation and technology adaptation”.

The government strictly regulates the cost and revenue structure of enterprises by implementing “high subsidies and strict penalties”: the net income of enterprises that actively transform (L₁ − C₁ + αG₁ − O₁ = 8 − 6 + 1.2 − 0.5 = 2.7 billion yuan) is much higher than that of enterprises that transform passively (L₂ − C₂ − μU = 2 − 1 − 0.6 = 0.4 billion yuan), promoting the convergence of enterprises’ strategies towards “active” transformation. Universities, due to the government’s research subsidies and the cooperation benefits with enterprises, cover the cost of active transformation C₃, forming a closed loop of “technology research–return of benefits”. Although consumers have a short-term preference for traditional purchases, government projects and mandatory requirements for university technology endorsements gradually reduce the cost θ of their green preference, laying the foundation for the system to evolve towards “consumer DG purchase”, and ultimately verifying the conclusion of the model that “strict regulation can drive the strategies of all parties to evolve towards a coordinated equilibrium”.

6. Numerical Simulation Analysis

6.1. Initial Simulation Parameter Settings

In order to more intuitively analyze the gradual stabilization trajectory of BMEs’ DG transformation path, the evolutionary game model described above was simulated using MATLAB based on the replicator dynamic equations and constraint conditions. Existing studies indicate that realism is not the primary focus of simulation; rather, the emphasis is on its usefulness and its ability to reveal the changing patterns of the system.

The initial values of the model involve parameters such as the costs and benefits of the game participants, government subsidies and regulatory costs for BMEs and universities, and the costs and benefits of enterprises’ proactive DGS transformation. These parameters are set according to the literature and field survey principles [62]. Other parameters are determined according to the equilibrium relationships among the main parameters [63].

For example, according to the literature and practical surveys, a total of CNY 1 billion in a DG economic innovation development fund was set up in Zhejiang Province in 2021 to support BMEs. Provinces such as Anhui, Guangdong, Sichuan, and Chongqing also established similar CNY 1 billion transformation and upgrade funds to support enterprises’ technological innovation and transformation projects; hence, the parameter G₁ is set to 10. Inner Mongolia provides subsidies of 20% of the actual equipment investment for smart factories and DG workshops [64]; thus, parameter α is set to 0.2. In Wenjiang District, Chengdu, subsidies of 20% of the revenue from DG consulting services provided by universities are offered, so parameter β is set to 0.2.

Additionally, according to the Data Security Law of the People’s Republic of China, institutions engaged in data transaction intermediary services that violate obligations without illegal gains can be fined between CNY 100,000 and 1 million, hence U = 100. The costs for BMEs when choosing proactive and passive DG transformation are denoted as C_i (i = 1, 2), and the penalty for breach of agreement between enterprises and universities is F. The expected benefits for consumers choosing DG or traditional consumption are R_i (i = 1, 2).

According to the equilibrium principle, the initial parameter settings satisfy the condition that the expected benefit of consumers choosing DG purchases is higher than that of traditional purchases, so consumers will eventually evolve toward the “DG purchase” [65]. Other initial parameter values, referring to actual conditions, are listed in

Table 9. Initial values of each parameter.

Parameter	λ	μ	γ	G2	G3	T	Z	H	L1	M	L2	O1
Assignment	0.5	0.5	0.3	2	5	10	8	1	4	2	3	2
Parameter	C3	C4	K1	K2	K3	W1	W2	W3	W4	O2	J	C5
Assignment	6	4	3	2	1	2	4	3	2	3	2	4

, and all parameters are set within a reasonable range.

6.2. Effects of Parameter Changes on BMEs’ DG Transformation Path

(1)

Effect of initial strategy choice on system evolution path.

Using Matlab simulations, the evolution of the decision-making behavior of the four game participants under the initial scenario—where all parties evolve toward probability 1 simultaneously—was analyzed. The simulation results of the initial system evolution game are shown in Figure 6. The horizontal axis represents time (t), and the vertical axis the government’s probability. BMEs, universities, and consumers choosing strict regulation are shown by (p), proactive DG transformation by (x), passive DG transformation by (y), and DG consumption by (z), respectively [66]. Furthermore, most government subsidies, environmental protection regulations and other policies are implemented on an annual basis (such as annual subsidy distribution and annual emission reduction assessment). Industry statistics (such as enterprise revenue and carbon emissions) are also calculated on an annual basis [23]. The DG transformation of BMEs involves digital infrastructure construction, green technology research and development, and the implementation of industry–universities–research cooperation, all of which are medium- and long-term projects (such as equipment renewal and technology iteration, which usually take 1–3 years). University research and development and the cultivation of consumers’ green preferences all require long-term accumulation (such as the transformation of university research results taking 1–2 years and the cultivation of consumer market demand taking several years) [31,53]. Measuring time in years can clearly show the time lag in strategic collaboration among the four parties (government, enterprises, universities, and consumers) (for example, enterprises reach stability first, and consumers reach stability later), avoiding the distortion of evolutionary logic caused by short cycles (such as months or quarters) [63]. Therefore, the time variable t is measured in years and represents the dynamic evolution process of the DG transformation system of the BME, reflecting the strategic adjustment cycles of the four major entities—the government, enterprises, universities, and consumers. The increase in the time variable t corresponds to the gradual learning process of each entity from the initial strategy (such as enterprises’ passive transformation and consumers’ traditional purchases) to the stable strategy (such as enterprises’ active transformation and consumers’ DG purchases), following the cycle of “strategy imitation–benefit feedback–optimization adjustment” (in line with the assumption of bounded rationality).

Assuming the initial probability set for the government, BME, university, and consumers choosing strict regulation, proactive DG transformation, passive DG transformation, and DG consumption is {0.5, 0.3, 0.2, 0.3} and that other parameters remain unchanged, the BME reach a stable point first at t = 0.3. Subsequently, the government, university, and consumers reach equilibrium at t = 0.6, 1, and 1.1, respectively. That is, the system achieves a stable state (1, 1, 1, 1) at t = 1.1, corresponding to the strategy set {strict regulation, proactive DG transformation, passive DG transformation, DG consumption} for the four participants. That is to say, in the first 0.3 years of the evolution process, the enterprise successfully achieves a stable strategy. After 1.1 years, the entire system (including the four parties) completes the convergence of the strategy and enters a long-term stable equilibrium state.

(2)

Effect of α on the quadruple evolutionary path.

Figure 7a shows that as the government subsidy coefficient for BMEs’ proactive DG transformation (α) gradually increases, the government decision-making time extends (from 0.6 years to 1.5 years), and when α ≥ 0.7, the final stable strategy shifts from strict regulation (p = 1) to lenient regulation (p = 0). An increase in α leads to an increase in government subsidy expenditure and a reduction in the critical value for strict regulation (z*). When α = 0.9, even if the probability of consumers’ DG purchases is at a medium level (z > 0.3), lenient regulation is more beneficial, which aligns with the condition z > z*. This indicates that higher regulatory intensity increases government costs, prompting the government to extend decision-making time to consider its own interests.

Figure 7b shows that after long-term evolution, BMEs adopt proactive DG transformation more rapidly and with shorter decision-making times, gradually stabilizing their strategy toward “proactive DG transformation.” As the government gradually increases the subsidy coefficient for BMEs’ proactive decarbonization transformation (α), the decision-making time for enterprises significantly shortens (from 0.3 years to 0.1 years), and the stable strategy converges to x = 1 more quickly; α directly reduces the active transformation cost (αG₁ increases) and lowers the threshold z** for active transformation. When α = 0.9, αG₁ is 9 billion yuan. Even with a low market demand, active transformation remains profitable, and the acceleration strategy converges. This suggests that increasing government subsidies effectively incentivizes enterprises to engage in proactive DG transformation.

Changes in α are not directly related to universities, so the evolutionary path and decision-making time of universities in Figure 7c remain largely unchanged. When α increases specifically, the decision-making time of the enterprise is significantly shortened (from 0.3 years to 0.1 years), and the stable strategy converges to x = 1 more quickly. α directly reduces the active transformation cost of the enterprise (αG₁ increases) and lowers the profit threshold z** for active transformation. When α = 0.9, αG₁ = 9 billion yuan. Even if the market demand is low, active transformation remains profitable and the acceleration strategy converges. Figure 7d shows that consumers’ decision-making time significantly decreases, indicating that enterprises’ choice of proactive DG transformation can influence consumers’ willingness to purchase DG products. Specifically, as α increases, the decision-making time for consumers shortens (from 1.1 years to 0.8 years), and enterprises can more quickly achieve proactive transformation, improving the supply and quality of DG products, enhancing consumer trust and perceived value, and indirectly promoting the evolution of purchasing behavior. Therefore, the government can appropriately increase DG R&D funding for enterprises to stimulate both enterprise transformation and consumer adoption.

(3)

Effect of β on the quadruple evolutionary path.

Figure 8a shows that as the government’s subsidy intensity for universities’ proactive DG transformation (β) gradually increases, the government’s strategy evolves from strict regulation toward relatively lenient regulation after long-term evolution. Specifically, when β increases and when β ≥ 0.7, the final government strategy shifts from strict regulation (p = 1) to lenient regulation (p = 0), and the decision-making time extends from 0.6 years to 1.4 years. An increase in β leads to an increase in government subsidy expenditures, but universities achieve active transformation more quickly, reducing regulatory costs (W₃ decreases). When z > z*, lenient regulation becomes more profitable. In this context, Figure 8c shows that universities adopt proactive DG transformation more rapidly, indicating a positive correlation between government subsidies and universities’ proactive DG behavior. The reason for this is that β directly increases the benefits of the universities’ proactive transformation (βG₁ increases), enabling the condition C₄ + F + W₂ + λU < C₃ + K₃ + O₂ + βG₁ to be met earlier, thereby driving the rapid evolution of the strategy.

Figure 8b shows that the decision-making time of BMEs gradually decreases, suggesting that higher β values strengthen universities’ willingness to engage in proactive DG transformation, which in turn encourages enterprises to adopt proactive DG strategies. Specifically, when β increases, the decision-making time of the enterprise shortens (from 0.3 years to 0.15 years). An increase in β enhances the willingness of universities to actively transform (y converges to 1 faster), improves the technical support and talent supply for enterprises, reduces the marginal cost of the enterprises’ active transformation, and accelerates the convergence of strategies. Moreover, changes in β are not directly related to consumers, so the evolutionary paths and decision times of consumers in Figure 8d remain largely unchanged.

(4)

Effect of λ on the quadruple evolutionary path.

As the government’s penalty intensity for universities’ passive DG transformation (λ) gradually increases, Figure 9c shows that universities’ decision-making time is significantly shortened, and after long-term evolution, universities adopt proactive DG transformation more rapidly. This indicates that higher government penalties for universities’ passive DG transformation clearly incentivize them to choose proactive strategies. The reason for this is that λ increases the cost of universities’ passive transformation (λU increases), strengthening the condition that C₄ + F + W₂ + λU < C₃ + K₃ + O₂ + βG₁, forcing the strategy to rapidly converge to the active transformation. Therefore, the government should impose sufficiently strong penalties on universities adopting passive DG strategies to ensure active DG transformation behavior.

Figure 9a shows that as λ increases, the government decision-making time extends from 0.6 years to 1.3 years. The final strategy involves strict supervision (p = 1). An increase in λ increases the penalty cost for universities’ passive transformation (λU increases) but does not reduce the government subsidy expenditure. When z < z*, strict supervision remains the optimal strategy. Moreover, changes in λ are not directly related to enterprises or consumers, so the evolutionary paths and decision times of BMEs and consumers in Figure 9b,d remain largely unchanged. The reason for this is that λ directly targets universities. The strategies of enterprises are mainly driven by their own revenue conditions (L₁ − C₁ − M + O₁ > L₂ − C₂ + αG₁), and this condition remains unchanged in this simulation. Externally, λ influences consumers through the technical support provided by universities. However, the simulation of the initial parameters ensures sufficient product trust, so there is no significant trend change.

(5)

Effect of μ on the quadruple evolutionary path.

As the government’s penalty intensity for BMEs’ passive DG transformation (μ) gradually increases, Figure 10b shows that the decision-making time of enterprises is significantly shortened, and after long-term evolution, enterprises adopt proactive DG transformation more rapidly. The reason for this is that μ increases the cost of enterprises’ passive transformation (μU increases), strengthens the condition L₂ − C₂ + αG₁ < L₁ − C₁ − M + O₁, and forces the strategy to rapidly converge to active transformation. Therefore, the government should impose sufficiently strong penalties on enterprises adopting passive DG strategies to ensure active DG transformation behavior.

Figure 10a shows that the government’s decision-making time increases significantly, indicating that enterprises’ passive DG transformation leads to intensified government regulation. Since the increase in μ raises the penalty costs for enterprises’ passive transformation (μU increases) but the government’s regulatory costs (W₁) do not significantly decrease, strict regulation remains the optimal strategy. Considering the interests of multiple stakeholders, the government inevitably extends its decision-making period. Moreover, changes in μ are not directly related to universities or consumers, so the evolutionary paths and decision times of universities and consumers in Figure 10c,d remain largely unchanged. μ directly targets enterprises. The strategy of universities is mainly driven by their own revenue conditions (βG₁ + M > C₃ − C₄), and this condition remains unchanged in this simulation. Furthermore, μ indirectly influences consumers through the quality of enterprises’ products. However, the simulation’s initial parameters ensure sufficient product trust, so there is no significant trend change.

(6)

Effect of γ on the quadruple evolutionary path.

As the government’s subsidy intensity for consumers’ DG consumption (γ) gradually increases, Figure 11d shows that after long-term evolution, consumers adopt DG consumption behavior more rapidly. This indicates that higher government subsidies significantly stimulate consumers’ DG consumption. When γ reaches 0.9, consumers ultimately choose DG consumption behavior. The reason for this is that γ directly increases consumer’s DG purchase benefits (γG₂ increases), strengthens the condition R₁ + γG₂ − (C₅ + θ) > R₂, and accelerates the evolution of the strategy. Therefore, government consumption subsidies substantially enhance consumers’ willingness to purchase DG products, facilitating the acceleration of DG production and lifestyle adoption. Moreover, Figure 11a shows that higher subsidies to consumers increase the government’s cost pressure. As γ increases from 0.1 to 0.9, the government gradually tends to adopt a lenient regulatory strategy. The reason for this is that an increase in γ enhances consumers’ DG purchasing behavior (where z converges to 1 more quickly), ensuring sufficient market demand (where z > z*) and facilitating more profitable lax regulation. Figure 11b,c indicate that the decision timing of BMEs and universities remains largely unchanged, which is consistent with the fact that government policies are targeted at consumers rather than enterprises or universities. γ directly targets consumers. The enterprise strategy is mainly driven by its own revenue conditions (L₁ − C₁ − M + O₁ > L₂ − C₂ + αG₁), and this condition remains unchanged in this simulation. The university strategy is mainly driven by its own revenue conditions (βG₁ + M > C₃ − C₄), and this condition remains unchanged in this simulation.

7. Conclusions and Future Directions

7.1. Conclusions

Under the context of the “dual carbon” strategy and the Digital China initiative, the building materials industry, as a typical high-energy-consumption and high-emission sector, faces a DG transformation that not only impacts its own sustainable development but also directly affects national energy structure optimization and the achievement of green and low-carbon goals. This study takes the government, BMEs, universities, and consumers as core analytical subjects and constructs a quadruple evolutionary game model of DG transformation. It systematically explores the strategy choices, interaction mechanisms, and equilibrium evolution paths among the stakeholders and validates the model’s dynamic stability and sensitivity to key parameters through numerical simulations. The main conclusions are summarized as follows.

First, there exist significant interdependence and strategy linkage among the four stakeholders in DG transformation. Government policy incentives and regulatory intensity serve as external drivers for enterprises’ DG transformation; enterprises’ technological innovation and investment decisions constitute the core driving force; universities provide technical support and talent supply as knowledge and intellectual foundations; and consumers’ green preferences and willingness to pay form a market feedback mechanism. The degree of coordination among these strategies determines whether the system can achieve stable evolution and high-quality equilibrium.

Second, the government’s regulatory intensity and incentive mechanisms play a dominant role in evolutionary stability. Model analysis indicates that when government regulation costs are low and subsidy and penalty mechanisms are reasonably configured, the system tends to evolve toward a stable state of “active government regulation–enterprises’ proactive transformation–university collaborative innovation–green consumer behavior.” Conversely, insufficient policy incentives or excessively high regulatory costs may lead to a non-cooperative equilibrium of “passive government–enterprises observing–low university efficiency–apathetic consumers.”

Third, enterprises’ digital capabilities and university research responsiveness act as mediating forces for transformation. Simulation results show that enhancing enterprise digital capabilities (increase in β coefficient) and strengthening university collaborative innovation (increase in μ coefficient) significantly reduces the time required for the system to reach stability and enhances the transmission efficiency of government policies, indicating that technological collaboration is a key path for achieving simultaneous DG transformation.

Fourth, consumers’ behavior is the ultimate driving force for the transformation of market orientation. When consumers receive government consumption subsidies (with γ increasing) or form a stable perception of the environmental value and digital service value of DG products through channels such as university technology popularization and enterprise digital disclosure, the probability of their green preferences (θ) converting into actual purchasing behavior significantly increases, thereby enhancing the market returns of enterprises’ green innovation. During this process, consumer decision-making is not merely a psychological tendency but rather a rational judgment based on “cost–benefit”. Policy incentives and information transparency jointly drive the system to evolve towards active equilibrium, highlighting the core role of the market-oriented mechanism on the demand side.

7.2. Implications

7.2.1. Theoretical Implications

This study provides several theoretical implications. First, it expands the systematic theoretical framework for DG transformation in BMEs. Previous studies largely focused on single-industry or single-stakeholder transformation paths in manufacturing or energy sectors and lacked a dynamic, system-level analysis for high-carbon industries. For instance, compared with the “government–enterprises–consumers” three-party evolutionary game framework constructed by Zhao et al. (2025) [28], this study is the first to incorporate universities into the analytical framework, filling the research gap of “the absence of technology supply entities”, revealing the core role of universities in knowledge innovation, talent cultivation and standard setting, and completing the theoretical loop of multi-party collaborative governance. Second, it deepens the theoretical logic of digital empowerment and green transformation synergy. Digital capabilities are not only a technological pathway for reducing energy consumption and carbon emissions but also critical variables reshaping resource allocation and organizational efficiency. Unlike the research by Yin and Zhao (2024), which focuses on the two-way game between the government and enterprises [30], this study reveals the synergistic mechanisms among policy incentives, technological innovation, and market feedback in the building materials value chain, offering a new perspective for understanding DG transformation in high-carbon sectors by constructing a quadruple evolutionary game model involving the government, enterprises, universities, and consumers. By treating digital empowerment as a mediating mechanism linking policy environment and green performance, this study establishes a “policy incentives–digital capabilities–green innovation” theoretical chain, enriching the dynamic game theory of enterprise transformation behaviors. Third, it uncovers new mechanisms of multi-stakeholder co-evolution in high-carbon industries. Evolutionary game analysis demonstrates significant positive feedback among government regulation, university innovation, enterprise response, and consumer preferences. Unlike traditional linear causal models, the quadruple evolutionary system emphasizes the dynamic interaction of strategy choices and the evolution toward equilibrium, providing empirical support for multi-stakeholder collaborative governance theory. Finally, compared with the tripartite game model for the green finance field proposed by Liu et al. (2024), this study has refined industry-specific parameters, such as transition costs, technological spillovers, and consumption preferences, based on the high-energy-consumption and high-emission characteristics of the building materials industry [36]. Moreover, by integrating replicator dynamics and Lyapunov stability theory, it provides methodological innovation for policy simulation and evolution research in the building materials industry, and it constructs a more industry-appropriate analytical framework, which can be used to study the dynamic balance in complex industrial systems.

7.2.2. Practical Implications

Given the characteristics of the Chinese system, policy design should take into account both central–local collaboration and regional differences and avoid losses in transformation efficiency due to imbalances in goal weighing or insufficient coordination. BMEs achieve green transformation through digitalization by adhering to the priority logic of “infrastructure construction first, application second; core elements first, collaboration later”. The core goal is to “replace factor-driven approaches with data-driven approaches”. Various measures will be implemented in stages and with emphasis on key areas. At the same time, the differentiated positioning and interaction mechanisms of government, universities, consumers, and industries will be clearly defined, in particular, establishing the core value of universities as an independent innovation entity and constructing a multi-party collaborative transformation ecosystem.

First, we implement the implementation path of DG transformation in priority order. In response to the actual challenges pointed out by Bashir et al. (2024), such as “insufficient demand for green building materials and high transformation costs” [33], this study proposes a three-stage path of “prioritizing infrastructure–achieving breakthroughs in core technologies–optimizing ecological synergy”. Through phased resource allocation, it effectively lowers the transformation threshold for small and medium-sized enterprises and makes up for the shortcomings of the “one-size-fits-all” policy recommendations in existing research [67]. The first stage involves prioritizizing the establishment of digital infrastructure to lay a solid foundation for transformation. The core task of this stage is to solve the fundamental problem of “lack of transformation support”, which has the strongest practicality and the highest marginal benefit. The government should lead the construction of three major infrastructure types: industrial internet platforms, energy digital monitoring networks, and supply chain data middle platforms. Differentiated support strategies should be implemented for leading enterprises and small and medium-sized enterprises in the BME industry: for leading enterprises, this involves focusing on subsidizing the establishment of cross-industry data middle platforms and encouraging the opening and sharing of data interfaces; for small and medium-sized enterprises, this involves providing low-cost digital transformation toolkits and cloud service support to lower the threshold for infrastructure construction. Simultaneously, the transformation of intelligent manufacturing units and the digitalization of energy management will be two core applications—prioritizing the transformation of high-energy-consuming and high-emission-production processes, achieving real-time monitoring and intelligent regulation of energy consumption through IoT sensors, and optimizing production scheduling through big data analysis to reduce unit output energy consumption. Supply chain digitalization will focus initially on upstream raw material traceability and downstream product low-carbon certification processes, temporarily not fully expanding to avoid resource dispersion. The second stage involves deepening technological integration and application to create differentiated competitive advantages. Based on the completion of infrastructure, the focus is on promoting the deep integration of artificial intelligence, big data, and green production, achieving a leap from “cost reduction and energy consumption reduction” to “value creation”. This includes prioritizing the layout of energy optimization systems based on artificial intelligence and supply chain low-carbon optimization models driven by big data: the former uses machine learning algorithms to mine energy-saving potential in the production process and achieve dynamic and precise energy regulation; the latter analyzes carbon emission data in each link of the supply chain to optimize procurement, logistics, and inventory strategies, reducing waste throughout the chain. The policy support in this stage should tilt towards “technology research and development and application”, providing tax credits and a step-by-step subsidy based on emission reduction effects for enterprises to purchase green digital technology equipment and conduct related technological research and development. To ensure the practicality and targeting of the policy, subsidies for purchasing green digital technology equipment and conducting related technological research and development should be provided. The third stage involves building a collaborative ecosystem to achieve low-carbon development throughout the entire industry. After the DG transformation at the enterprise level begins to show results, the focus shifts to the construction of an industry-coordinated digital ecosystem, promoting the transformation from “single-point breakthrough” to “system upgrade”. Led by industry leaders, upstream and downstream enterprises, universities, and digital service providers will jointly build the “DG-Innovation” ecosystem, with the core being the establishment of a data-sharing and benefit distribution mechanism—clearly defining the scope, authority, and revenue-sharing rules of data sharing, and optimizing the entire production, circulation, and consumption process through collaborative governance. The policy focus in this stage is to improve the supporting systems of the ecosystem, such as establishing data security supervision norms and formulating unified low-carbon data accounting standards for the industry, to ensure the sustainability of the collaborative model.

Second, compared with the research of Wang et al. (2025), which merely emphasized the role of government procurement policies in promoting green building materials [24], this study optimizes the government’s differentiated dynamic policy system and establishes a progressive policy mechanism of “base subsidy–performance reward–severe penalty”. It avoids “one-size-fits-all” subsidies and penalties, links subsidies to emission reduction effects, tightens penalties according to the gradient of the transformation stage, and incorporates university technology transfer incentives and consumer preference guidance. This forms a multi-dimensional policy synergy, enhancing the policy’s precision and sustainability and improving the policy’s precision and guidance. On one hand, it involves implementing differentiated incentive mechanisms to precisely match the transformation stage and enterprise type. For the infrastructure construction in the first stage, pre-incentives will be implemented to provide 30–50% purchase subsidies for enterprises when they purchase industrial internet equipment and energy monitoring systems. For the technical integration application in the second stage, result-oriented rewards will be implemented, where enterprises will receive tiered bonuses based on their actual emission reduction and production efficiency improvement. At the same time, low-interest green credit will be provided, with the credit interest rate linked to the carbon emission reduction performance of the enterprises. For collaborative research and development projects, a special fund will be established to provide matching subsidies for the R&D investment of low-carbon materials and carbon capture, utilization, and storage (CCUS) technologies jointly tackled by universities and enterprises [67]. On the other hand, a dynamic supervision mechanism will be established, implementing a gradually tightened constraint standard. A “graded emission limit” will be constructed, reducing the energy consumption and emission benchmarks of the BME industry year by year. The penalty for high-energy-consuming and high-emission enterprises will gradually increase over time—initially, it will be mainly through rectification notices and moderate fines; in the middle stage, an additional carbon emission excess tax will be imposed; and in the long term, enterprises that refuse to transform will be subject to production restrictions or exit mechanisms. At the same time, a dynamic adjustment of the enterprise classification list will be established, updated in real time based on the progress of the enterprises’ green transformation, ensuring the flexibility of the policy.

Third, in response to the issue raised by AlJaber et al. (2023) [21] regarding the “lack of technical support for the circular economy transformation in the building materials industry”, this study clarified the positioning of universities as “independent innovation entities”, fully leveraging their role as the core engine of green innovation. Through participation in the entire chain of “basic research–technology transformation–standard formulation”, it solved the problem of “disconnection between industry, academia, and research”, providing a practical solution for the precise alignment of technological innovation with industrial demands. Universities are not merely tools for policy implementation, but independent entities in the DG transformation of BMEs, serving as the source of technological innovation, a talent training base, and an industry standard setter. Their roles are manifested in three core dimensions. First, as an independent innovation entity, they should focus on cutting-edge fields such as low-carbon material research, energy-saving process innovation, and carbon capture, utilization, and storage (CCUS) technology, and conduct basic and forward-looking research to break through the technical bottlenecks of BMEs’ green transformation. Unlike the application-oriented R&D of enterprises, universities’ research focuses more on underlying technological innovation, such as developing new low-carbon composite materials suitable for BME-production and carbon-footprint-accounting models based on artificial intelligence, providing original technical solutions for industry transformation. Second, as a collaborative research and development link, they should promote the commercialization of technologies. Universities should actively take the lead in establishing research and development cooperative platforms instead of passively accepting enterprise commissions. Through the establishment of joint laboratories and technology transfer centers, they can precisely match laboratories’ research results with enterprises’ production needs. For example, in response to the energy optimization requirements of enterprises in intelligent manufacturing, universities can convert the developed energy-saving algorithms into commercially available software systems, achieve commercialization through technology licensing, equity investment, etc., and use the obtained profits to support research, forming a “research–transformation–re-research” virtuous cycle. Third, as a talent cultivation and standard-setting entity, they provide long-term intellectual support. Universities, based on the DG transformation needs of the BME industry, will set up interdisciplinary majors in intelligent manufacturing and green low-carbon technology, cultivating comprehensive talents with digital technology capabilities and green development concepts, providing professional talent reserves for the industry. At the same time, by leveraging their academic neutrality and professional authority, they will lead in formulating evaluation standards for the DG transformation of the BME industry, including carbon-footprint accounting methods, intelligent manufacturing energy efficiency standards, etc., guiding the industry towards standardized development.

Fourth, in contrast to Asif et al. (2024), who only focused on research on internal innovation capabilities of enterprises, this study constructs a multi-agent collaborative ecosystem, emphasizing the breaking of information barriers between upstream and downstream industries through data sharing and benefit distribution mechanisms, achieving a breakthrough from “single-point transformation of enterprises” to “collaborative upgrading of the entire industrial chain”, providing an operational implementation path for the overall low-carbon development of the industry [6]. The construction of an industry-level collaborative digital ecosystem requires the principle of “data sharing, mutual benefit, and risk sharing”, breaking the information barriers among entities. Led by the industry association, together with enterprises, upstream and downstream companies of the BME industry chain, universities, and digital service providers, a “DG-Innovation” ecosystem platform is jointly established: enterprises are responsible for providing actual data in the production and circulation processes, universities are responsible for providing technical support and standard formulation, and digital service providers are responsible for the technical operation and upgrade of the platform; at the same time, an income distribution mechanism is established. For the achievements realized through data sharing in terms of emission reduction and efficiency improvement, the contributions of each entity are divided according to the proportion of work performed, ensuring the long-term stable operation of the ecosystem and ultimately achieving collaborative low-carbon development throughout the production, circulation, and consumption processes.

7.3. Limitations and Future Directions

This study constructs a quadruple evolutionary game model of DG transformation with the government, BMEs, universities, and consumers as the main stakeholders, and it uses numerical simulations to reveal the evolutionary patterns of the system under different strategy combinations. However, several limitations remain. The model assumptions are relatively idealized, not fully accounting for information asymmetry among stakeholders or time-lag effects in policy implementation; future research could incorporate heterogeneous agents or incomplete information game models to improve realism. Parameter settings are primarily based on policies and industry data from typical regions, which limits generalizability; subsequent studies could calibrate the model using more micro-level samples or cross-regional empirical data. Moreover, this study focuses on the domestic building materials industry and does not consider the influence of international green supply chains and carbon border adjustment mechanisms; future research should explore policy coordination and market interactions from a global perspective to enrich the theoretical framework of DG transformation in high-carbon industries. Overall, this study provides a systematic analytical framework for the collaborative governance of BMEs’ DG transformation, and future research could further deepen the understanding of multi-stakeholder dynamic feedback and policy synergy mechanisms, offering more forward-looking theoretical insights and practical guidance for high-quality industrial development.