EVOLUTIONARY GAME ANALYSIS OF LOW-CARBON TRANSFORMATION OF CONSTRUCTION ENTERPRISES UNDER THE "DUAL CARBON" TARGET

Purpose: This study aims to investigate the impacts of different choices made by construction enterprises, government, and the public on the low-carbon transformation of Chinese construction enterprises in the context of the global climate crisis. Theoretical framework: The main theoretical foundation of this research is the theory of dynamic evolutionary games, it can aptly reflects the dynamic evolutionary process of strategy choices by various stakeholders during the promotion of low-carbon construction. Method/design/approach: This study adopts a mixed-method approach involving literature review, qualitative analysis, and quantitative analysis. Firstly, a payoff matrix is constructed for the three stakeholders under different strategy choices. Then, the conditions under which different strategies tend to reach equilibrium are discussed. Finally, the stability of equilibrium solutions in evolutionary game is analyzed. Results and conclusion: There are 7 equilibrium solutions that can be evolutionary stable strategies in specific situations. It is challenging for the system to achieve a progressively stable strategy when only one or two entities participate in low-carbon transformation. Research implications: This study focuses on the background of the Chinese government's "dual carbon" target. It takes an innovative approach by considering the stakeholders in the low-carbon building supply chain, including the government and the general public, and develops a tripartite evolutionary game model for the low-carbon transformation of construction enterprises. This research makes a significant contribution to the future development of low-carbon buildings in China. Originality/value: The results obtained in this study are unprecedented, innovative and relevant to the scientific community, in the context of sustainable development of low-carbon buildings.


INTRODUCTION
According to the "BP Statistical Review of World Energy 2022|71st edition" , China's carbon emissions in 2022 were 10,866.8×106 tons, accounting for 32.07% of the world's total carbon emissions. It's energy consumption was 157.65EJ, accounting for 26.50% of global energy consumption. As the world's largest emitter of carbon dioxide and consumer of energy, China faces enormous pressure to reduce its carbon emissions.
The Chinese government has always attached great importance to the development of low-carbon economy and the protection of the earth's ecology. On September 22, 2020, Chinese President Xi Jinping solemnly declared at the 75th United Nations General Assembly that "China will adopt more powerful policies and measures, and strive to peak carbon dioxide emissions before 2030 and achieve carbon neutrality before 2060." In July 2021, the "Implementation Plan for Carbon Peaking in the Urban and Rural Construction Industry" was issued, which pointed out that the urban and rural construction industry is one of the main areas of carbon emissions, and the growth of carbon emissions in this field should be controlled to ensure that the carbon emissions in the urban and rural construction industry reach their peak before 2030, and the comprehensive green and low-carbon transformation of the urban and rural construction industry is achieved before 2060. In October 2021, the Chinese government emphasized in the "Report of the 20th National Congress of the Communist Party of China" that "China should actively and steadily promote the realization of the carbon peak and carbon neutrality goals, 'Green' is an intrinsic requirement for China's development in the next five years".
According to the "2022 China Building Energy Consumption and Carbon Emissions Research Report", the total carbon emissions of the entire process of Chinese construction in 2020 were 5.08 billion tons of CO2, accounting for 50.9% of the national total. Despite the Chinese government's high regard for the development of low-carbon and green buildings, there 3 are still many obstacles to achieving the goal of "carbon peaking by 2030 and carbon neutrality by 2060".Promoting the low-carbon transformation of China's construction industry is an effective way to solve the contradiction between the development of the construction industry and environmental protection. Government participation in low-carbon building supply chain management can effectively reduce building carbon emissions and save energy. The effective implementation of low-carbon buildings requires the participation of relevant parties, including the government, construction enterprises, and the general public.
This study aims to provide insights into the inherent patterns, influencing factors, and stable equilibrium strategies of low-carbon transformation in Chinese construction enterprises by constructing a tripartite evolutionary game model involving the government, construction enterprises, and the public. By studying the strategic choices of stakeholders, it seeks to contribute to the understanding of how to promote low-carbon buildings, reduce greenhouse gas emissions, and improve government regulatory mechanisms, among other related issues.

THEORETICAL REFERENCES
Domestic and foreign scholars have conducted extensive research on the low-carbon transformation of architectural enterprises and reducing carbon emissions in the building production process.
In 1928, John von Neumann established the fundamental principles of game theory, which marked the formal birth of the theory. Evolutionary game theory is a theory based on bounded rationality and limited information that emphasizes dynamic equilibrium and does not require participants to be perfectly rational. Cohen et al.(2017) used a prisoner's dilemma model to study the barriers to greenhouse gas emissions reduction in the Israeli construction industry and concluded that government agencies should provide incentives to both builders and consumers in order to promote the construction of high-level green buildings. Ding et al. (2018) developed an environmental benefit assessment model for construction waste reduction management using system dynamics. Chen and Hu (2018) used evolutionary game theory to analyze the behavioral strategies of governments and manufacturers under different carbon taxes and subsidies. Lu et al. (2019) considered government reputational costs and constructed a three-party game model among the government, construction enterprises, and consumers to study the mutual influences among the three parties during the low-carbon transformation of construction enterprises. Fan and Hui (2020) analyzed the decision-making mechanisms of governments and developers on green building incentives using evolutionary game theory. Macêdo et al.(2021) conducted a questionnaire analysis to examine the impact of environmental responsibility on the performance of municipal governments and local community management. Kosanoglu and Kus (2021) studied the sustainability level of the supply chain management in the Turkish construction industry based on the building lifecycle theory, adopting the triple sustainability dimensions of "environment, society, and economy". Gao et al. (2022) used evolutionary game theory to simulate the development of green buildings based on dynamic government subsidies. Lu et al. (2022) analyzed decision-making behaviors and management mechanisms for construction and demolition waste recycling based on publicprivate partnership.Additionally, Li et al. (2022) investigated China's Jinshan Yinshan sustainability evolutionary game equilibrium research under government and enterprises resource constraint dilemma, while Garcia et al. (2023) examined the influence of social and environmental responsibility of construction enterprises on environmental sustainability by analyzing the key factors impacting the environment during the construction process of residential buildings in Brazil, Mexico, and the United States.
Currently, there are few studies on low-carbon transformation of construction enterprises under the background of "dual carbon". The low-carbon transformation of Chinese construction 4 enterprises is a long-term and dynamic process, in which the government, as a policy maker (supervisor), and the public, as "low-carbon consumers," play important roles in enterprise transformation. Therefore, incorporating the government and the public into a three-party evolutionary game model of low-carbon transformation of construction enterprises will better reflect the dynamic evolution process of strategic choices among all stakeholders in the promotion of low-carbon construction.

METHODOLOGY
This study employed a combination of literature review, qualitative analysis, and quantitative analysis. Firstly, published papers and books were reviewed to analyze the relevant theoretical background of the research subject. Then, utilizing evolutionary game theory, the study introduced government subsidies and public participation as additional utilities and constructed a tripartite evolutionary game model for the low-carbon transformation of construction enterprises involving the government, construction enterprises, and the general public. Finally, the stability of equilibrium solutions in the evolutionary game was analyzed. The findings of this study provide insights for optimizing government policies in China and are of significant practical importance for promoting the low-carbon transformation of the construction industry.

Problem Description
Low-carbon development of the construction industry involves many stakeholders, who can be divided into individual and collective stakeholders. This paper attempts to construct an evolutionary game model of low-carbon transformation of construction enterprises involving the government, construction enterprises, and the public, starting from the supply and demand collective stakeholders in the low-carbon building supply chain. The interest framework of the three parties is shown in Figure 2.  The Chinese government plays an important role as the maker and supervisor of lowcarbon building transformation policies, guiding building enterprises to achieve low-carbon transformation by adopting administrative measures such as formulating standards, tax control, and subsidy incentives. Although these measures can enhance the credibility of the government, they also bring significant financial pressure due to high regulatory costs.
Construction enterprises are the main actors in low-carbon emissions reduction, and their decision to undergo a low-carbon transformation is often influenced by government policies and public opinion on environmental protection. When deciding whether to pursue low-carbon transformation, construction enterprises are also affected by the costs of the transformation as well as the public's demand for low-carbon buildings.
The public is the main consumer of low-carbon buildings and also an informal regulator of low-carbon environments. Whether the public chooses to purchase low-carbon building products directly affects the production of low-carbon buildings and the circular development of the entire supply chain. However, the public's preferences for low-carbon consumption are different, so it is crucial to promote the public's active purchase of low-carbon products.
Therefore, as stakeholders in low-carbon construction, the government, construction enterprises, and the public mutually influence and constrain each other's strategic choices. The low-carbon transformation of construction enterprises is a dynamic game process of three parties under their respective interest motivations, from conflict and adjustment to equilibrium.

Model Assumptions
The low-carbon building supply chain involves multiple participating entities. This paper selects a simplified supply chain composed of the government, construction enterprises, and the public for analysis. Based on stakeholder theory and evolutionary game theory, the following assumptions are made: Assumption 1: All three parties are limited rational individuals with learning ability, and information is not fully symmetrical among them.
Assumption 2: All three parties make independent decisions based on maximizing their own interests.
Assumption 3: During the development process of the low-carbon transformation of the construction enterprises, the three parties dynamically adjust their decisions until an evolutionarily stable strategy is achieved.
Assumption 4: The decision of the public to choose low-carbon products is mainly influenced by product prices. 6 Assumption 5: The low-carbon products produced by the construction enterprises through transformation have no difference in appearance and quality compared to the original products.
The government has two strategies, actively regulating and not regulating, with probabilities of x and 1-x respectively. The government's strategy space is G (regulation, nonregulation); Construction enterprises have two strategies, low-carbon transformation and no transformation, with probabilities of y and 1-y respectively. The construction enterprises's strategy space is C (low-carbon transformation, non-low-carbon transformation); The public has two strategies, choosing to participate in the purchase of low-carbon buildings or not, with probabilities of z and 1-z respectively. The public's strategy space is P (participation, nonparticipation). Where x, y, and z ∈ [0,1] are functions of time, and there are a total of eight game strategy combinations among the supply chain participants.

Parameter Setting
4.3.1 Government's cost-benefit variables 1 R g :The government's basic revenue refers to the fiscal income obtained through taxes and other means when it does not regulate the carbon emissions of the construction industry. 2 R g :The government's potential revenue refers to the credibility and public support it gains from actively regulating low-carbon production in the construction industry. 3 R g :The government's derivative revenue refers to the positive impact its actions have on the long-term development of the natural environment under regulatory decisions. 1 C g :The government's transfer payments to enterprises refer to the support it provides to low-carbon transformation construction enterprises under regulatory decisions, such as reducing taxes and providing subsidies.  7 enterprises adopts a low-carbon production mode in a social environment with better environmental protection awareness, which increases the market share. 3 R c :The derivative revenue of a construction enterprises refers to the increasing intangible benefits, such as reputation and opportunities, gained from technology upgrading and low-carbon transformation under government regulation. 1 C c :The basic cost of a construction enterprises refers to the basic expenses incurred in carrying out construction-related production activities. 2 C c :The additional cost of a construction enterprises refers to the cost incurred in technology innovation and product development when undergoing low-carbon transformation. 3 C c :The opportunity cost of a construction enterprises refers to the opportunity loss of the enterprises when not choosing low-carbon transformation, such as the loss of additional government support for construction enterprises that do not undergo low-carbon transformation.
4.3.3 The public's cost-benefit variables 1 R p :The basic utility of the public refers to the utility obtained when purchasing products from construction companies. 2 R p :The additional utility of the public refers to the satisfaction brought by making a low-carbon building purchase decision when the public has a higher awareness of environmental protection. 1 C p :The potential loss of the public refers to the extra cost incurred when choosing to purchase low-carbon building products compared to regular building products in the absence of government regulation. 2 C p :The opportunity cost of the public refers to the cost incurred when the public participates in environmental pollution control when construction companies do not undergo low-carbon transformation.

Model Construction
Based on the parameter settings, the payoff matrix for the three-player game of lowcarbon transformation and evolution in construction enterprises can be obtained (see Tables 3  and 4).      Due to the information asymmetry among the government, construction enterprises, and the public, all three parties in the game will adjust their strategies through learning and imitation. Based on the payoff matrix, the expected revenue functions of the government, construction enterprises, and the public in the game model of low-carbon transformation and evolution in construction enterprises can be obtained.

Expected revenue of the government
The expected revenue of the government is g1 E when actively regulated, g2 E when not regulated, and the average revenue of the government in this game model is denoted as g E , expressed as follows:

Expected revenue of construction enterprises
The expected revenue of construction enterprises is c1 E when engaging in low-carbon transformation, c2 E when not engaging in low-carbon transformation, and the average revenue of construction enterprises in this game model is denoted as c E , expressed as follows:

Expected revenue of the public
The expected revenue of the public is p1 E when participating in low-carbon behavior, p2 E when not participating in low-carbon behavior, and the average revenue of the public in this game model is denoted as p E , expressed as follows: Based on the Malthusian dynamic equation, can derive the replicator dynamic equations for the government, construction enterprises, and the public. The equations are as follows:

Stability Analysis of Evolutionary Game
Based on the tripartite replication dynamic equation of the game constructed in section 4.4, equilibrium strategy analysis can be carried out.
By setting , the boundary of the evolutionary game can be obtained: From the above equation, it can be derived that:

Analysis of the Strategy Stability of the Government
x is an equilibrium point. That is, when the benefits of government regulation are less than the costs, based on the assumption of "rational economic agents," the government tends to choose the "non-regulation" strategy. When neither of the above two conditions is met, there are two further cases iii) and iv).
iii) When 1 3 2 3 2 x is an equilibrium point. In this case, the government will still tend to choose the "non-regulation" strategy. iv) When 1 3 2 3 2 x is an equilibrium point. In this case, when the benefits of government regulation are greater than the regulatory costs, the government tends to choose the "regulation" strategy.

Analysis of the Strategy Stability of the Construction Enterprises
That is, when the benefits of low-carbon transformation for construction enterprises exceed those of not undertaking such a transformation, based on the assumption of "rational economic agents", construction enterprises are tend to choose the strategy of "low-carbon transformation". When neither of the above two conditions is met, there are two further cases iii) and iv). 12 are less than the costs of undertaking such a transformation, the construction enterprises are likely to choose the strategy of "non-low-carbon transformation".

Analysis of the Strategy Stability of the Public
.At this point, the proportion of the public strategy selection remains stable and is not affected by time changes. ii) When In this case,when the benefits of the public's participation in purchasing low-carbon buildings exceed the benefits of not participating, based on the assumption of "rational economic agents," the public tends to choose the "participation" strategy. When neither of the above two conditions is met, there are two further cases iii) and iv).
iii) When 2 1 ,thus 1 = z is an equilibrium point.In this case,when the benefits of the public's participation in purchasing low-carbon buildings exceed the benefits of not participating, the public is still tend to choose the "participation" strategy. iv) When 2 1 2 2 2 1 g p ,thus 0 = z is an equilibrium point.When the benefits of the public's participation in purchasing low-carbon buildings cannot offset the additional costs incurred by this behavior, the public will not participate in the low-carbon transformation process of building enterprises. That is, when the benefits of the public's participation in purchasing low-carbon buildings are less than the benefits of not participating, the public tends to choose the "non-participation" strategy.

Stability Analysis of Evolutionary Game Equilibrium Solutions
The replicator dynamic equations (10)~(12) reflect the process of strategic game selection by interest entities with bounded rationality through learning and simulation. In the process of group dynamic evolution, it is difficult to directly judge which equilibrium solution the government, construction enterprises, and consumers will ultimately tend to. However, the local stability of the group evolution equilibrium point can be analyzed by the Jacobian matrix. The Jacobian matrix of the system of this model is as follows: 13 By setting up Equations (10) to (12), i.e., the replicator dynamic equations of the government, Construction enterprises,and the public, and letting: It can be seen from the above equation that there are a total of 8 equilibrium solutions, namely Firstly, we analyze equilibrium point ) 1 , 1 , 1 ( 1 E , and the Jacobian matrix at this point is: The stability of the equilibrium solutions can be analyzed using the Lyapunov indirect method. When ) R R ( are both positive and negative, is a saddle point. Similarly, the asymptotic stability of other equilibrium points can be obtained. In summary, in the tripartite subjects evolutionary game model of low-carbon transformation of construction enterprises, there are cases where the eigenvalues of the Jacobian matrix of are all negative, indicating that the seven equilibrium points can be evolutionary stable strategies under specific circumstances. However, in the system, it is difficult to achieve an asymptotically stable strategy when only one or two parties participate in the low-carbon transformation of construction. In the scenario where the government supervises, construction enterprises actively transform, and the public participates extensively ( 14 supervises, construction enterprises actively transform, and the public participates extensively, the game model can achieve an ideal stable state.

RESULTS AND DISCUSSION
The low-carbon transformation of construction enterprises is one of the important means to achieve China's "carbon peaking and carbon neutrality" goals. The proposal of the "dual carbon" target provides an opportunity for the construction industry to transform from a traditional mode to a green, low-carbon, and sustainable development mode, but at the same time, it poses a huge challenge for traditional construction enterprises.
This paper introduces the additional benefits of government subsidies and public participation and constructs a game-theoretical model for the low-carbon transformation of building enterprises involving Tripartite Subjects: government, building enterprises, and the public . Firstly, the payment matrix is established for the government, building enterprises, and the public under different strategic choices. Then, the conditions for the strategic equilibrium of Tripartite Subjects are discussed, and finally, the stability of the equilibrium solution of the evolutionary game is analyzed. The study shows that there are seven equilibrium solutions that can be evolutionarily stable in specific circumstances of the model. However, it is difficult for the system to achieve gradually stable strategies when only one or two parties participate in low-carbon transformation. The dynamic game will ultimately evolve into the ideal outcome of "government regulation, construction enterprises low-carbon transformation, and active public participation" only when certain conditions are met. These conditions and results can provide ideas for the policy optimization of low-carbon transformation of Chinese construction enterprises.

CONCLUSION
In response to global warming, the Chinese government has solemnly proposed the dual carbon targets of "carbon peaking" and "carbon neutrality". As one of China's three pillar industries, the low-carbon transformation process of the construction industry is crucial.Despite the government's issuance of some documents to support the research and promotion of lowcarbon technologies in the construction industry through tax incentives and subsidies, the overall Chinese construction industry still remains in a traditional mode of high energy consumption and high carbon emissions.
This study we starts from the supply and demand groups of stakeholders in the lowcarbon construction supply chain, and lead into government subsidies and the added utility of public participation, and construct a evolutionary game model for the low-carbon transformation of construction enterprises with the participation of government, construction enterprises and the public.This study effectively captures the collective behavior of construction enterprises in their low-carbon transformation under the conditions of government and public participation. It accurately reflects the behavioral interactions among enterprises, government, and the public, providing insights into the dynamic evolution process of strategic choices by various stakeholders during the promotion of low-carbon buildings.
Based on the research results, we propose the following suggestions for the low-carbon transformation of China's construction industry: (1) The government should increase environmental protection publicity efforts to raise public awareness of environmental protection, increase support for enterprises lowcarbon transformation, moderately reduce regulatory costs, and fully play its leading role.
(2) Whether construction enterprises choose to transform to low-carbon production depends on the balance between their costs and benefits. Only when the benefits of 15 transformation outweigh the costs will enterprises actively engage in transformation. Construction enterprises should enhance their sense of social responsibility, fully recognize their role as the main body in low-carbon transformation, and assume their own social responsibilities.
(3)The behavior of the general public to participate in low-carbon environmental protection activities is easily influenced by the strategies of other actors. Therefore, the government should increase publicity efforts, improve the participation of the public in regulatory systems, accelerate the construction of a regulatory system for environmental protection involving public participation, and take other measures to increase public engagement in low-carbon environmental protection behavior.