Low-Carbon Construction in China’s Construction Industry from the Perspective of Evolutionary Games

Abstract

Industrialization and increased energy use are leading to a greater influence of environmental and climate challenges on human existence and progress. China’s emissions in 2023 totaled 12.6 gigatons, representing 35% of global emissions, establishing it as the top carbon emitter globally. Combined with China’s industrial structure, it is essential to investigate carbon reduction in the building sector due to its significant contribution to carbon emissions. This study introduces a third-party organization into the relationship between stakeholders, based on traditional government regulation. It constructs a three-party dynamic evolution model involving the government, environmental protection organization, and construction enterprise. The study analyzes the evolution process of the three-party strategy selection using evolutionary game theory. We analyze the elements influencing decision-making for the three parties through simulation analysis and provide appropriate recommendations. The study’s findings indicate that low-carbon construction in China’s construction sector is an intricate system involving several stakeholders, each guided by their own interests when determining their behavioral methods. Government penalties and financial subsidies can influence construction enterprises to adopt low-carbon production practices to some degree, but excessive rewards and punishments may not support system stability.

1. Introductory

Environmental and climate governance has been a significant issue for the international community due to globalization and the interconnectedness of human fate. Climate warming is leading to increased occurrences of extreme weather, melting glaciers, and increasing sea levels, posing a threat to human society’s production and development. To mitigate climate change, it is crucial to decrease greenhouse gas emissions promptly. Carbon dioxide is the most detrimental greenhouse gas [1]. Over 130 parties globally have announced commitments to achieve “zero carbon” or “carbon neutral” status since the Paris Agreement [2]. Various regions and governments have also put in place low-carbon legislation and systems [3,4,5,6]. The government encourages low-carbon growth through the implementation of command-based and market-based environmental rules [7]. It has implemented required measures to restrict corporate air pollution emissions, established a carbon emissions trading system (ETS) for corporations to trade carbon emission quotas, and offered financial incentives to encourage emission reduction [8,9].

China’s carbon emissions have stayed elevated because of its industrial composition [10]. Chinese President Xi Jinping declared during the 2020 United Nations General Assembly that China aims to achieve carbon neutrality by 2030 and carbon neutrality by 2060 [11,12]. This promise presents a significant challenge to China’s internal energy, technology, and economy. The Global Carbon Dioxide Emissions Report (2023) [13], published by the International Energy Agency (IEA), shows that while carbon emissions are decreasing in sophisticated economies worldwide, China’s emissions have reached 12.6 Gt in 2023, representing 35% of global emissions. China, being one of the world’s major CO₂ emitters, is under significant pressure due to carbon emissions and must promptly implement low-carbon construction. In response, China has implemented many laws and strategies to encourage low-carbon construction. These involve enhancing energy production, modernizing energy consumption methods, and innovating carbon-neutral technologies. The construction industry is a big carbon emitter and a major consumer of energy among many businesses contributing to carbon emissions [14,15]. China’s extensive history of consistent investment in infrastructure and real estate underscores the need to prioritize emission reduction in the building sector [16,17]. The China Building Energy Consumption Research Report (2022) states that in 2020, buildings in China were responsible for 50.9% of the country’s total carbon emissions [18]. Construction businesses play a significant role in greenhouse gas emissions. It is crucial for them to regulate their production practices to lessen environmental impact and support sustainable growth [19,20,21].

Advancing low-carbon construction in the sector requires more than just individual efforts; the involvement and understanding of stakeholders are essential. Evolutionary game theory is commonly employed to analyze the dynamics of interactions among distinct groups [22]. Evolutionary game theory has been extensively utilized in other sectors such as energy [23], agriculture [24], ecological governance [25], and food safety [26], and it is also relevant to this study. Existing studies on study subjects have recognized the significant impact of government regulation and aim to investigate the interest dynamics between the government and other entities [27,28,29]. Some scientists suggest that technical innovation can effectively decrease carbon emissions, and they include evolutionary game theory into green building research [30]. Qiang Du et al., focus on the advantages of low-carbon coordination in developer–stakeholder interactions [31]. Qingfeng Meng et al., examine how government rewards and penalties change during green building construction [32]. Yu Liu et al., focus on the interconnections between the government, suppliers, and developers in the green building supply sector [33]. Some experts argue that low-carbon production by businesses deserves more social attention. Nan Feng and colleagues argue that efficient fiscal policies can facilitate businesses’ transition to environmentally friendly and low-carbon practices [34]; Guohua Qu and his team view downstream enterprises as a target for government oversight [35]; Dongsheng Liu and his team assert that government subsidies positively impact enterprise innovation [36].

Most research on low-carbon construction in firms is not inside the construction industry; instead, the construction field tends to focus on technological innovation. This study focuses on construction enterprises as the primary research subjects and examines the regulatory influence of the government. Building firms are highly susceptible to engaging in negative green production behaviors due to cost and profit concerns, given the extended life cycle and significant investment associated with building projects. Hence, apart from government control, enhancing social oversight should be taken into account. This study examines how a third-party environmental protection organization can act as a regulator to investigate low-carbon construction practices within complex relationships of multiple interests [37]. The goal is to identify strategies for boosting the green productivity of construction companies.

2. Model Assumptions and Construction

2.1. Underlying Assumptions

In order to study the game relationship between the three subjects, the following assumptions need to be made first:

Assumption 1. 

In this study, the government, environmental protection organizations and construction enterprises are the three parties of the game, and all of them show limited rationality and repeat the game a limited number of times.

Assumption 2. 

The government’s strategy is a = (a₁, a₂) = (strict regulation, not strict regulation), the probability of choosing “strict regulation” is x, and the probability of choosing “not strict regulation” is 1 − x, in which 0 ≤ x ≤ 1. The strategy of the environmental organization is b = (b₁, b₂) = (active regulation, inactive regulation), the probability of choosing “active regulation” is y, and the probability of choosing “inactive regulation” is 1−y, where 0 ≤ y ≤ 1. The strategy of the construction company is c = (c₁, c₁) = (low-carbon construction), the probability of choosing “low-carbon construction” is c = (c₁, c₁) = (low-carbon construction, non-low-carbon construction), the probability of choosing “low-carbon construction” is c, and the probability of choosing “non-low-carbon construction” is 1−c, where 0 ≤ c ≤ 1.

Hypothesis 3. 

When the government chooses “strict regulation”, it needs to pay the regulatory cost F while at the same time obtaining potential benefits R in terms of public satisfaction and government credibility. The government’s regulatory strength is α (0 < α < 1).

Hypothesis 4. 

When the environmental organization chooses to “actively regulate”, it pays the regulatory cost L and at the same time receives donations from the public Q₁, incentives and subsidies from the government S₂, as well as potential benefits such as public recognition and social honor Q₂. When the environmental organization fails to carry out its regulatory duties and environmental pollution occurs due to the non-low-carbon construction of the construction company, the environmental organization receives the benefits Q₂, which is the result of its failure to perform its regulatory duties. Through environmental pollution, environmental organizations gain potential losses such as social reputation and popular word-of-mouth D.

Hypothesis 5. 

The construction company hires green innovative talents, adopts low-carbon building materials, new environmental protection and energy saving technologies, etc., pays the cost E₁, reaps the benefits of low-carbon construction C₁, and receives the rewards of tax incentives and financial subsidies from the government due to the potential benefits B. The construction company chooses to adopt non-low-carbon construction, which costs E₂, and receives the benefits C₂, E₂, and E1. The cost of choosing “non-low-carbon construction” is E₂, the benefit is C₂, and E₁ < E₂, C₁ < C₂. If the process of non-low-carbon construction leads to environmental pollution, governments need to bear the cost of environmental governance T and impose a fine on the construction company, P. At the same time, if environmental organizations choose to regulate aggressively, their protests against non-low-carbon choices by construction firms can lead to a loss of U in terms of public pressure on construction firms to stop work and rectify the situation, as well as a loss of industry word-of-mouth and public reputation.

The model symbols are shown in

Table 1. Model symbols.

Model Symbols	Meaning	Note
$F$	Regulatory costs to the government
$R$	Potential gains from government regulation
$T$	Costs to the government of combating environmental pollution caused by non-low-carbon construction by construction companies
$S_1$	Government incentives for construction companies that choose low-carbon construction
$S_2$	Government funding for incentives for environmental organizations to participate in regulation
$P$	Penalties for construction firms found by the government to not be carrying out low-carbon construction
$L$	Regulatory costs for environmental organizations
$Q_1$	Funding from public donations for active regulation by environmental organizations
$Q_2$	Potential benefits of active regulation by environmental organizations
$U$	Environmental groups use fierce protests to take a toll on construction firms
D	Environmental organizations do not regulate and companies are not low-carbon, leading to potential losses to environmental organizations
$E_1$/$E_2$	Costs of low-carbon/non-low-carbon construction by construction firms	$E_1>E_2$
$C_1$/$C_2$	Benefits of low-carbon/non-low-carbon construction by construction companies	$C_1<C_2$
$B$	Potential benefits to the government from low-carbon construction by construction companies
α	Government regulatory effort factor	0 ≤ α ≤ 1

.

2.2. Modeling

Based on the above assumptions, a strategy game matrix can be established, with the government, environmental organizations, and construction companies as the main three parties, as shown in

Table 2. Tripartite behavioral strategy mix and benefit matrix for the government, environmental organizations, and construction companies.

				Construction Company
				Low-Carbon Construction	Non-Low-Carbon Construction
government	strict supervision	environmental organization	active supervision	$a_1$: $R-F-S_1-S_2+B$ $b_1$: $S_2-L+Q_1+Q_2$ $c_1$: $S_1+C_1-E_1$	$a_1$: $R-F-T-S_2+P$ $b_1$: $S_2-L+Q_1+Q_2$ $c_2$: $-P-U+C_2-E_2$
			not actively regulated	$a_1$: $R-F{-S}_1+B$ $b_2$: 0 $c_1$: $S_1+C_1-E_1$	$a_1$: $R-F-T+P$ $b_2$: −D $c_2$: $-P+C_2-E_2$
	not strictly regulated	environmental organization	active supervision	$a_2$: $\alpha R-\alpha F-\alpha S_1-{\alpha S}_2+B$ $b_1$: ${\alpha S}_2-L+Q_1+Q_2$ $c_1$: $\alpha S_1+C_1-E_1$	$a_2$: $\alpha R-\alpha F-T-{\alpha S}_2+P$ $b_1$: ${\alpha S}_2-L+Q_1+Q_2$ $c_2$: $-P-U+C_2-E_2$
			not actively regulated	$a_2$: $\alpha R-\alpha F-\alpha S_1+B$ $b_2$: 0 $c_1$: $\alpha S_1+C_1-E_1$	$a_2$: $\alpha R-\alpha F-T+P$ $b_2$: −D $c_2$: $-P+C_2-E_2$

.

3. Model-Specific Analyses

The following dynamic equations for replication and strategy stability analysis are used to replicate the behavioral strategies of the government, environmental organizations, and construction companies, respectively.

3.1. Analysis of the Stability of the Government’s Strategy

If the expected return to the government for choosing “strict regulation” is $T_{11}$, and the expected return to the government for choosing “less strict regulation” is $T_{12}$, then

$$\begin{array}{l}{T}_{11}=yz(R-F-S_1-S_2+B)+y(1-z)(R-F-T-S_2+P)+(1-y)z(R-F-S_1+B)+(1-y)\\ \hspace{1em}\hspace{0.17em}(1-z)(R-F-T+P)\end{array}$$

$$\begin{array}{l}{T}_{12}=yz(\alpha R-\alpha F-\alpha S_1-\alpha S_2+B)+y(1-z)(\alpha R-\alpha F-T-\alpha S_2+P)+(1-y)z\\ \hspace{1em}\hspace{0.17em}(\alpha R-\alpha F-\alpha S_1+B)+(1-y)(1-z)(\alpha R-\alpha F-T+P)\end{array}$$

If the average expected return to the government is T₁, then

$$T_1=x{T}_{11}+(1-x)T_{12}$$

If the replication dynamic equation for the government strategy choice is F(x), then

$$F(x)=dx/dt=-x(\alpha -1)(x-1)(F-R+S_{2}y+S_{1}z).$$

The first order derivative function of F(x) is

$$d(F(x))/dt=(1-2x)(\alpha -1)(F-R+S_{2}y+S_{1}z)$$

Lead $G(y)=(\alpha -1)(F-R+S_{2}y+S_{1}z)$ when G(y) = 0 and y = y⁰.

According to the stability theorem of the differential equation, the government’s strategy choice to be in a stable state must satisfy F(x) = 0 and F′(x) < 0. Since ∂G(y)/∂y < 0, it can be seen that G(y) is a decreasing function with respect to y. The government’s strategy choice must be in a stable state. Therefore, when y = y⁰, F(x) = 0 and d(F(x))/dt = 0, at which time the government is unable to determine a stabilizing strategy; when y < y⁰, G(y) > 0, at which time F(x) = 0 and d(F(x))/dt|_x=1 < 0; then, x = 1 is in a stable state; when y > y⁰, G(y) < 0, at which time F(x) = 0 and d(F(x))/dt|_x=0 < 0; then, x = 0 is in a steady state. The evolutionary phase diagram of the government’s strategy choice is shown in Figure 1.

As shown in Figure 1, the probability that the government chooses to strictly regulate is the volume of the V_x1 portion, and the probability that the government chooses not to strictly regulate is the volume of the V_x2 portion, which is calculated as follows:

$$V_{x2}=\underset{0}{\overset{1}{{\displaystyle \int }}}\underset{0}{\overset{1}{{\displaystyle \int }}}\frac{F-R+S_{1}z}{-S_2}dxdz=\frac{2F-2R+S_1}{-2S_2}$$

$$V_{x1}=1-V_{x2}$$

Corollary 1. 

The probability that the government chooses to strictly regulate is negatively correlated with respect to the cost that the government has to pay in the process of regulation and the incentives that the government gives to the construction companies that choose low-carbon construction and the environmental organizations that choose to actively regulate, and it is positively correlated with respect to the benefits that can be obtained from the regulation.

Proof. 

According to the expression of the probability V_x1 that the government chooses to strictly regulate, the first-order partial derivation of F, R, S₁, and S₂ can be obtained as follows: ∂V_x1/∂F < 0, ∂V_x1/∂R > 0, ∂V_x1/∂S₁ < 0, ∂V_x1/∂S₂ < 0. Therefore, a decrease in F, S₁, and S₂ or a rise in R can make the probability that the government chooses to strictly regulate increase. □

If environmental organizations choose to regulate aggressively, their protests against non-low-carbon choices by construction firms can lead to a loss of U in terms of public pressure on construction firms to stop work and rectify the situation, as well as a loss of industry word-of-mouth and public reputation, whereas the potential benefits that can be gained from the government’s regulatory behavior, such as government credibility and people’s satisfaction, can increase the government’s enthusiasm for active regulation.

3.2. Strategic Stability Analysis of Environmental Organizations

If the expected benefit to environmental organizations of choosing ‘active regulation’ is T₂₁, and the expected benefit to environmental organizations of choosing ‘inactive regulation’ is T₂₂, then

$$\begin{array}{l}{T}_{21}=xz(S_2-L+Q_1+Q_2)+x(1-z)(S_2-L+Q_1+Q_2)+(1-x)z(\alpha S_2-L+Q_1+Q_2)+(1-x)\\ \hspace{1em} (1-z)(\alpha S_2-L+Q_1+Q_2)\\ T_{22}=x(1-z)(-D)+(1-x)(1-z)(-D)\end{array}$$

If the average expected return for environmental organizations is T₂, then

$$T_2=y{T}_{21}+(1-y)T_{22}$$

If the replication dynamic equation for the choice of environmental organization strategy is F(y), then

$$F(y)=dy/dt=-y(y-1)(D-L+Q_1+Q_2+\alpha S_2-Dz+S_{2}x-\alpha S_{2}x).$$

The first-order derivative function of F(y) is

$$d(F(y))/dt=(1-2y)(D-L+Q_1+Q_2+\alpha S_2-Dz+S_{2}x-\alpha S_{2}x)$$

Lead $G(z)=(D-L+Q_1+Q_2+\alpha S_2-Dz+S_{2}x-\alpha S_{2}x)$ when G(z) = 0 and z = z⁰.

According to the stability theorem of the differential equation, the environmental protection organization’s strategy selection to be in a stable state must satisfy F(y) = 0 and F′(y) < 0. Since ∂G(z)/∂z < 0, it can be seen that G(z) is a decreasing function on z. Therefore, when z = z⁰, F(y) = 0 and d(F(y))/dt = 0, at which time the environmental organization is unable to determine a stabilization strategy. When z < z⁰, G(z) > 0, at which time F(y) = 0 and d(F(y))/dt|_y=1 < 0; then, y = 1 is in the stabilization state. When z > z⁰, G(z) < 0, at which time F(y) = 0 and d(F(y))/dt|_y=0 < 0; then, y = 0 is in a steady state. The evolutionary phase diagram of the strategy choice of the environmental organization is shown in Figure 2.

As shown in Figure 2, the probability that an environmental organization chooses to actively regulate is calculated as the volume of the V_y1 fraction, and the probability that it chooses not to actively regulate is calculated as the volume of the V_y2 fraction:

$$V_{y1}=\underset{0}{\overset{1}{{\displaystyle \int }}}\underset{0}{\overset{1}{{\displaystyle \int }}}\frac{D-L+Q_1+Q_2+\alpha S_2+S_{2}x-\alpha S_{2}x}{D}dxdy=\frac{2D-2L+2Q_1+2Q_2+\alpha S_2+S_2}{2D}$$

Corollary 2. 

The probability that an environmental organization chooses to actively regulate is positively related to the potential gains from public donations, public recognition, and social honor, as well as the rewards from the government that it receives after choosing to actively regulate, and it is also positively related to the potential losses of the environmental organization if it chooses not to actively regulate and if the construction firm’s non-low-carbon construction leads to environmental damage, but it is negatively related to the costs of participation in the regulation that it incurs. Human, material, and financial costs are negatively correlated.

Proof. 

According to the expression of the probability of active regulation chosen by environmental protection organizations V_y1, the first-order partial derivation of D, L, Q₁, Q₂, and S₂ can be obtained as follows: ∂V_y1/∂D > 0, ∂V_y1/∂L < 0, ∂V_y1/∂Q₁ > 0, ∂V_y1/∂Q₂ > 0, and ∂V_y1/∂S₂ > 0. Therefore, the probability that an environmental organization chooses to regulate aggressively increases as L falls or as D, Q₁, Q₂, and S₂ rise. □

3.3. Strategic Stability Analysis of Construction Companies

If the expected return for a construction company choosing “low-carbon construction” is T₂₁, and the expected return for a government choosing “non-low-carbon construction” is T₂₂, then

$$T_{31}=xy(S_1+C_1-E_1)+x(1-y)(S_1+C_1-E_1)+(1-x)y(\alpha S_1+C_1-E_1)+(1-x)(1-y)(\alpha S_1+C_1-E_1)$$

$$\begin{array}{l}{T}_{32}=xy(-P-U+C_2-E_2)+x(1-y)(-P+C_2-E_2)+(1-x)y(-P-U+C_2-E_2)+(1-x)(1-y)\\ \hspace{1em} (-P+C_2-E_2)\end{array}$$

If the average expected return of a construction firm is T₂, then

$$T_3=z{T}_{31}+(1-z)T_{32}$$

If the replicated dynamic equation for the strategy choice of a construction firm is F(z), then

$$F(z)=dz/dt=-z(z-1)(C_1- C_2-E_1+E_2+P+\alpha S_1+S_{1}x+Uy-\alpha S_{1}x).$$

The first-order derivative function of F(z) is

$$d(F(z))/dt=(1-2z)(C_1-C_2-E_1+E_2+P+\alpha S_1+S_{1}x+Uy-\alpha S_{1}x)$$

Lead $G(x)=(C_1- C_2-E_1+E_2+P+\alpha S_1+S_{1}x+Uy-\alpha S_{1}x)$ when G(x) = 0 and x = x⁰.

According to the stability theorem of the differential equation, the strategy selection of the construction enterprise to be in a stable state must satisfy F(z) = 0 and F′(z) < 0. Since ∂G (x)/∂x > 0, it can be known that G(x) is an increasing function regarding x. Therefore, when x = x⁰, F(z) = 0 and d(F(z))/dt = 0; at this time, the construction company cannot determine the stabilization strategy. When x < x⁰, G(z) < 0; at this time, F(z) = 0 and d(F(z))/dt|_z=0 < 0; then, z = 0 is in the stabilization state. When x > x⁰, G(z) > 0; at this time, F(z) = 0 and d(F(z))/dt|_z=1 < 0; then, z = 1 is in a steady state. The evolutionary phase diagram of the strategy choice of the construction firm is shown in Figure 3.

As shown in Figure 3, the probability of a construction firm choosing low-carbon construction is calculated as the volume of the V_z1 portion, and the probability of choosing non-low-carbon construction is calculated as the volume of the V_z2 portion:

$$V_{z1}=\underset{0}{\overset{1}{{\displaystyle \int }}}\underset{0}{\overset{1}{{\displaystyle \int }}}\frac{C_1-C_2-E_1+E_2+P+\alpha S_1+Uy}{\alpha S_1-S_1}dxdy=\frac{2C_1-2C_2-2E_1+2E_2+2P+2\alpha S_1+U}{2(\alpha -1)S_1}$$

Corollary 3. 

The probability of a construction enterprise choosing low-carbon construction is positively correlated with the benefits gained from low-carbon construction, the cost of choosing non-low-carbon construction, the government’s rewards and penalties, and the losses incurred by environmental organizations due to their protests against the choice of non-low-carbon construction, and it is negatively correlated with the cost of low-carbon construction and the benefits of non-low-carbon construction.

Proof. 

According to the expression of the probability V_z1 of the construction enterprise choosing low-carbon construction, the first-order partial derivation of C₁, C₂, E₁, E₂, P, S₁, and U can be obtained as follows: ∂V_z1/∂C₁ > 0, ∂V_z1/∂C₂ < 0, ∂V_z1/∂E₁ < 0, ∂V_z1/∂E₂ > 0, ∂V_z1/∂P > 0, ∂V_z1/∂ S₁ > 0, and ∂ V_z1/∂U > 0. Therefore, when C₁, E₂, P, S₁, and U are gradually raised, the probability of construction companies choosing low-carbon construction is also raised. Conversely, if C₂ and E₁ are progressively raised, the probability of a construction company choosing low-carbon construction decreases. □

3.4. System Equilibrium and Stability Analysis

The Jacobian determinant of the three-way evolutionary game is known to be

$$\mathrm{j}=\left[\begin{array}{ccc} \frac{\partial F(x)}{\partial x}& \frac{\partial F(x)}{\partial y}& \frac{\partial F(x)}{\partial z}\\ \frac{\partial F(y)}{\partial x}& \frac{\partial F(y)}{\partial y}& \frac{\partial F(y)}{\partial \mathrm{z}}\\ \frac{\partial F(z)}{\partial x}& \frac{\partial F(z)}{\partial y}& \frac{\partial F(z)}{\partial z}\end{array}\right]$$

Based on the tripartite replication of the dynamic equations for the government, environmental organizations, and construction companies, letting F(x) = 0, F(y) = 0, and F(z) = 0, eight system pure strategy equilibrium points can be obtained, including ${\mathrm{A}}_1(0,0,0),{\mathrm{A}}_2(1,0,0),{\mathrm{A}}_3(0,1,0),{\mathrm{A}}_4(0,0,1),{\mathrm{A}}_5(1,1,0),{\mathrm{A}}_6(1,0,1),{\mathrm{A}}_7(0,1,1),{\mathrm{A}}_8(1,1,1)$. The eigenvalues obtained by bringing these eight equilibria into the Jacobian matrix are shown in

Table 3. Equilibrium points and their corresponding eigenvalues.

Balance Point	Eigenvalue (Math)
	δ1	δ2	δ3
${\mathrm{A}}_1(0, 0, 0)$	$\mathrm{R} - \mathrm{F}+\mathrm{\alpha }\mathrm{F} - \mathrm{\alpha }\mathrm{R}$	$\mathrm{D} - \mathrm{L}+{\mathrm{Q}}_1+{\mathrm{Q}}_2+\mathrm{\alpha }{\mathrm{S}}_2$	${\mathrm{C}}_1 - {\mathrm{C}}_2 - {\mathrm{E}}_1+{\mathrm{E}}_2+\mathrm{P}+\mathrm{\alpha }{\mathrm{S}}_1$
${\mathrm{A}}_2(1, 0, 0)$	$\mathrm{F} - \mathrm{R} - \mathrm{\alpha }\mathrm{F}+\mathrm{\alpha }\mathrm{R}$	$\mathrm{D} - \mathrm{L}+{\mathrm{Q}}_1+{\mathrm{Q}}_2+{\mathrm{S}}_2$	${\mathrm{C}}_1 - {\mathrm{C}}_2 - {\mathrm{E}}_1+{\mathrm{E}}_2+\mathrm{P}+{\mathrm{S}}_1$
${\mathrm{A}}_3(0, 1, 0)$	$\mathrm{L} - \mathrm{D} - {\mathrm{Q}}_1 - {\mathrm{Q}}_2 - \mathrm{\alpha }{\mathrm{S}}_2$	$\mathrm{R} - \mathrm{F} - {\mathrm{S}}_2+\mathrm{\alpha }\mathrm{F} - \mathrm{\alpha }\mathrm{R}+\mathrm{\alpha }{\mathrm{S}}_2$	${\mathrm{C}}_1 - {\mathrm{C}}_2 - {\mathrm{E}}_1+{\mathrm{E}}_2+\mathrm{P}+\mathrm{U}+\mathrm{\alpha }{\mathrm{S}}_1$
${\mathrm{A}}_4(0, 0, 1)$	${\mathrm{Q}}_1 - \mathrm{L}+{\mathrm{Q}}_2+\mathrm{\alpha }{\mathrm{S}}_2$	$\mathrm{R} - \mathrm{F} - {\mathrm{S}}_1+\mathrm{\alpha }\mathrm{F} - \mathrm{\alpha }\mathrm{R}+\mathrm{\alpha }{\mathrm{S}}_1$	${\mathrm{C}}_2 - {\mathrm{C}}_1+{\mathrm{E}}_1 - {\mathrm{E}}_2 - \mathrm{P} - \mathrm{\alpha }{\mathrm{S}}_1$
${\mathrm{A}}_5(1, 1, 0)$	$\mathrm{L} - \mathrm{D} - {\mathrm{Q}}_1 - {\mathrm{Q}}_2 - {\mathrm{S}}_2$	$\mathrm{F} - \mathrm{R} + {\mathrm{S}}_2 - \mathrm{\alpha }\mathrm{F}+\mathrm{\alpha }\mathrm{R} - \mathrm{\alpha }{\mathrm{S}}_2$	${\mathrm{C}}_1 - {\mathrm{C}}_2 - {\mathrm{E}}_1+{\mathrm{E}}_2+\mathrm{P}+\mathrm{U}+{\mathrm{S}}_1$
${\mathrm{A}}_6(1, 0, 1)$	${\mathrm{Q}}_1 - \mathrm{L}+{\mathrm{Q}}_2+{\mathrm{S}}_2$	${\mathrm{C}}_2 - {\mathrm{C}}_1+{\mathrm{E}}_1 - {\mathrm{E}}_2 - \mathrm{P} - {\mathrm{S}}_1$	$\mathrm{F} - \mathrm{R} + {\mathrm{S}}_1 - \mathrm{\alpha }\mathrm{F}+\mathrm{\alpha }\mathrm{R} - \mathrm{\alpha }{\mathrm{S}}_1$
${\mathrm{A}}_7(0, 1, 1)$	$\mathrm{L} - {\mathrm{Q}}_1 - {\mathrm{Q}}_2 - \mathrm{\alpha }{\mathrm{S}}_2$	${\mathrm{C}}_2 - {\mathrm{C}}_1+{\mathrm{E}}_1 - {\mathrm{E}}_2 - \mathrm{P} - \mathrm{U} - \mathrm{\alpha }{\mathrm{S}}_1$	$\mathrm{R} - \mathrm{F} - {\mathrm{S}}_1 - {\mathrm{S}}_2+\mathrm{\alpha }\mathrm{F} - \mathrm{\alpha }\mathrm{R}+\mathrm{\alpha }{\mathrm{S}}_1+\mathrm{\alpha }{\mathrm{S}}_2$
${\mathrm{A}}_8(1, 1, 1)$	$\mathrm{L} - {\mathrm{Q}}_1 - {\mathrm{Q}}_2 - {\mathrm{S}}_2$	${\mathrm{C}}_2 - {\mathrm{C}}_1+{\mathrm{E}}_1 - {\mathrm{E}}_2 - \mathrm{P} - \mathrm{U} - {\mathrm{S}}_1$	$\mathrm{F} - \mathrm{R} + {\mathrm{S}}_1+{\mathrm{S}}_2 - \mathrm{\alpha }\mathrm{F} + \mathrm{\alpha }\mathrm{R} - \mathrm{\alpha }{\mathrm{S}}_1 - \mathrm{\alpha }{\mathrm{S}}_2$

.

Scenario 1. 

The point A₁ indicates that the government chooses not to strictly regulate, environmental organizations choose not to actively regulate, and construction companies choose to build in a non-low-carbon manner. The stabilization conditions for this point are $\mathrm{R}+\mathrm{\alpha }\mathrm{F} < \mathrm{\alpha }\mathrm{R}+\mathrm{F}$,  $\mathrm{D} + {\mathrm{Q}}_1+{\mathrm{Q}}_2+\mathrm{\alpha }{\mathrm{S}}_2<\mathrm{L}$, and ${\mathrm{C}}_1+{\mathrm{E}}_2+\mathrm{P}+\mathrm{\alpha }{\mathrm{S}}_1<{\mathrm{C}}_2+{\mathrm{E}}_1$.

Scenario 2. 

The point A₂ indicates that the government chooses to strictly regulate, environmental organizations choose not to actively regulate, and construction companies choose non-low-carbon construction. The stability conditions for this point are $\mathrm{F}+\mathrm{\alpha }\mathrm{R}<\mathrm{R} + \mathrm{\alpha }\mathrm{F}$, $\mathrm{D} + {\mathrm{Q}}_1+{\mathrm{Q}}_2+{\mathrm{S}}_2<\mathrm{L}$, and ${\mathrm{C}}_1+{\mathrm{E}}_2+\mathrm{P} + {\mathrm{S}}_1<{\mathrm{C}}_2+{\mathrm{E}}_1$.

Scenario 3. 

The point A₃ indicates that the government chooses not to regulate strictly, environmental organizations choose to regulate actively, and construction firms choose to build in a non-low-carbon manner. The point is stabilized conditionally: $\mathrm{L}<\mathrm{D} + {\mathrm{Q}}_1+{\mathrm{Q}}_2+\mathrm{\alpha }{\mathrm{S}}_2$, $\mathrm{R}+\mathrm{\alpha }\mathrm{F}+\mathrm{\alpha }{\mathrm{S}}_2<\mathrm{F} + \mathrm{\alpha }\mathrm{R} + {\mathrm{S}}_2$, and  ${\mathrm{C}}_1+{\mathrm{E}}_2+\mathrm{P}+\mathrm{U}+\mathrm{\alpha }{\mathrm{S}}_1<{\mathrm{C}}_2+{\mathrm{E}}_1$.

Scenario 4. 

The point A₄ indicates that the government chooses not to strictly regulate, environmental organizations choose not to actively regulate, and construction firms choose to build in a low-carbon manner. The point is stabilized conditionally: ${\mathrm{Q}}_1+{\mathrm{Q}}_2+\mathrm{\alpha }{\mathrm{S}}_2<\mathrm{L}$, $\mathrm{R}+\mathrm{\alpha }\mathrm{F}+\mathrm{\alpha }{\mathrm{S}}_1<\mathrm{F} + {\mathrm{S}}_1+\mathrm{\alpha }\mathrm{R}$, and ${\mathrm{C}}_2+{\mathrm{E}}_1<{\mathrm{C}}_1+{\mathrm{E}}_2+\mathrm{P}+\mathrm{\alpha }{\mathrm{S}}_1$.

Scenario 5. 

The point A₅ indicates that the government chooses to strictly regulate, environmental organizations choose to actively regulate, and construction companies choose to build in a non-low-carbon manner. The point is stabilized conditionally: $\mathrm{L}<\mathrm{D} + {\mathrm{Q}}_1+{\mathrm{Q}}_2+{\mathrm{S}}_2$, $\mathrm{F} + {\mathrm{S}}_2+\mathrm{\alpha }\mathrm{R}<\mathrm{R} + \mathrm{\alpha }\mathrm{F} + \mathrm{\alpha }{\mathrm{S}}_2$, and ${\mathrm{C}}_1+{\mathrm{E}}_2+\mathrm{P}+\mathrm{U} + {\mathrm{S}}_1<{\mathrm{C}}_2+{\mathrm{E}}_1$.

Scenario 6. 

The point A₆ indicates that the government chooses to strictly regulate, environmental organizations choose not to actively regulate, and construction firms choose to build in a low-carbon manner. The point is stabilized conditionally: ${\mathrm{Q}}_1+{\mathrm{Q}}_2+{\mathrm{S}}_2<\mathrm{L}$,  ${\mathrm{C}}_2+{\mathrm{E}}_1<{\mathrm{C}}_1+{\mathrm{E}}_2+\mathrm{P} + {\mathrm{S}}_1$, and  $\mathrm{F} + {\mathrm{S}}_1+\mathrm{\alpha }\mathrm{R}<\mathrm{R} + \mathrm{\alpha }\mathrm{F} + \mathrm{\alpha }{\mathrm{S}}_1$.

Scenario 7. 

The point A₇ indicates that the government chooses not to regulate strictly, environmental organizations choose to regulate actively, and construction companies choose to build in a low-carbon manner. The point is stabilized conditionally: $\mathrm{L}<{\mathrm{Q}}_1+{\mathrm{Q}}_2+\mathrm{\alpha }{\mathrm{S}}_2$, ${\mathrm{C}}_2+{\mathrm{E}}_1<{\mathrm{C}}_1+{\mathrm{E}}_2+\mathrm{P}+\mathrm{U}+\mathrm{\alpha }{\mathrm{S}}_1$, and $\mathrm{R}+\mathrm{\alpha }\mathrm{F}+\mathrm{\alpha }{\mathrm{S}}_1+\mathrm{\alpha }{\mathrm{S}}_2<\mathrm{F} + {\mathrm{S}}_1+{\mathrm{S}}_2+\mathrm{\alpha }\mathrm{R}$.

Scenario 8. 

The point A8 indicates that the government chooses to strictly regulate, environmental organizations choose to actively regulate, and construction companies choose to build in a low-carbon manner. The point is stabilized by the following condition: $\mathrm{L}<{\mathrm{Q}}_1+{\mathrm{Q}}_2+{\mathrm{S}}_2$, ${\mathrm{C}}_2+{\mathrm{E}}_1<{\mathrm{C}}_1+{\mathrm{E}}_2+\mathrm{P}+\mathrm{U} + {\mathrm{S}}_1$, and $\mathrm{F} + {\mathrm{S}}_1+{\mathrm{S}}_2+\mathrm{\alpha }\mathrm{R}<\mathrm{R} + \mathrm{\alpha }\mathrm{F} + \mathrm{\alpha }{\mathrm{S}}_1+\mathrm{\alpha }{\mathrm{S}}_2$.

4. Simulation Analysis

4.1. System Stability Check

In order to further explore the mechanisms and factors affecting the selection of the three-party game strategy, numerical simulation is carried out using MATLAB R2023a software. According to the literature data and combined with the real situation, the construction enterprises need to pay more costs to meet the low-carbon construction standards, while the low-carbon construction benefits are often greater than the non-low-carbon construction benefits, and the difference between the two costs is greater than the difference between the benefits. On the basis of a middle value of 0.5 for the coefficient α of the government’s supervisory strength, two sets of parameters are set to meet the stability conditions of the points according to the needs of the experimental simulation, as follows:

Array I: F = 5, R = 30, T = 30, S₁ = 25, S₂ = 5, P = 15, L = 7, Q₁ = 5, Q₂ = 10, U = 20, D = 10, E₁ = 100, E₂ = 80, C₁ = 30, C₂ = 40, and B = 30. The results of the numerical simulation test are shown in Figure 4.

Array I: F = 5, R = 30, T = 30, S₁ = 15, S₂ = 5, P = 15, L = 7, Q₁ = 5, Q₂ = 10, U = 20, D = 10, E₁ = 100, E₂ = 80, C₁ = 30, C₂ = 40, and B = 30. The results of the numerical simulation are shown in Figure 5.

4.2. Effects of Parameter Changes

In order to better explore the importance of each parameter that affects the change in the system, the parameter settings are varied to investigate the mechanism of their influence using array II as a baseline.

(1)

Impact of tripartite costs on system evolution

The cost of government regulation is assigned as F = 5, F = 15, and F = 20; the cost of environmental protection organization regulation is assigned as L = 7, L = 15, and L = 30; and the cost of low-carbon construction for construction enterprises is assigned as E₁ = 80, E₁ = 100, and E₁ = 120, respectively. At the same time, the initial probability of the strategy selection of the three-party subject is set as (0.3, 0.1, 0.1), and the replicated system of dynamic equations is simulated 50 times for evolution over time. The simulation results of 50 times of time evolution are shown in Figure 6, Figure 7, and Figure 8, respectively.

In Figure 6, it can be seen that the system evolution is stable when F = 5 and at the point (0, 1, 1) when F = 15 and F = 20. The speed of the government’s evolution towards a less stringent regulatory strategy increases when F increases. When F = 15, the government evolves towards strict regulation upfront but eventually chooses to stabilize at less strict regulation. This indicates that the government is initially willing to invest in regulation, but the cost of regulation is too large, resulting in negative regulation.

As can be seen in Figure 7, when L goes from 7 to 15, the evolution of environmental organizations’ decision-making towards positive regulation slows down significantly, especially when L = 30; the environmental organizations ultimately choose not to actively regulate. At the same time, the strategic choice of environmental protection organizations affects the construction enterprises to a certain extent, and when environmental protection organizations gradually tend towards negative regulation, the evolution speed of construction enterprises choosing low-carbon construction also gradually decreases.

As can be seen in Figure 8, the tripartite system quickly stabilizes at the point (1, 1, 1) when E₁ = 80, and the evolution speed slows down slightly when E₁ is raised to 100, but it eventually remains stable at the point (1, 1, 1). However, after E₁ is raised to 120, the strategy choices of construction companies rapidly shift towards non-low-carbon construction, while the strategy choices of the remaining two parties remain unchanged. This indicates that even under the supervision of the government and environmental organizations, construction corporations opt out of low-carbon construction when they deem the costs to be excessive, prioritizing profit over environmental concerns.

It can be seen that cost is an important factor influencing the strategy choice of the three parties, and the lower the cost is, the strategy of the three parties moves faster in a positive direction.

(2)

The effect of government rewards and punishments on the system

The government’s rewards and penalties are changed for the remaining two parties. The incentive funds given to environmental protection organizations for active regulation were assigned as S₂ = 5, S₂ = 10, and S₂ = 15. The rest of the parameter settings are the same as above, and the final system simulation results are shown in Figure 9. Tax incentives for governments to choose low-carbon construction, financial support, and other subsidies were assigned as S₁ = 5, S₁ = 15, and S₁ = 30, the rest of the parameter settings were the same as those above, and the final system simulation results are shown in Figure 10. The government’s penalties for non-low-carbon construction enterprises were assigned to P = 15, P = 30, and P = 60, and the rest of the parameter settings were the same as those above. The final system simulation results are shown in Figure 11.

As can be seen in Figure 9, in the process of S₂ gradually increasing, the decision-making of environmental protection organizations gradually tends towards the evolution of positive regulation, and vice versa. The government’s enthusiasm to participate in regulation is greatly reduced. It can be seen that at S₂ = 15, the decision-making evolution of the system is stable at (0, 1, 1). This indicates that enhancing the government’s reward for environmental organizations’ participation in regulation is certainly conducive to enhancing their motivation, but it has a negative impact on the government’s own decision-making.

As can be seen in Figure 10, in the process of S₁ gradually increasing, the speed of the construction enterprises choosing low-carbon construction also gradually increases. In S₁ = 5, the construction enterprises have a tendency to evolve to the non-low-carbon construction, indicating that the construction enterprises, out of the pursuit of their own higher interests, may choose the non-low-carbon construction, but the participation of the remaining two parties in the regulation can effectively affect their decision-making. Therefore, at S₁ = 30, construction companies decisively choose low-carbon construction, Over-subsidizing construction corporations could strain the government’s finances, thereby prompting the government to consider deregulation., letting the system evolution finally stabilize at the point (0, 1, 1).

As can be seen in Figure 11, the higher the value of P, the faster the evolution of construction firms choosing low-carbon construction. The evolution curve of x to 1 at P = 15 is once flat at the beginning, indicating that under the low penalty, the construction enterprises may not be willing to carry out low-carbon construction, but under the influence of the remaining two decision-making parties, the decision-making of the construction enterprises eventually evolves in a positive direction.

It can be seen that a moderate increase in the government’s rewards and penalties for environmental organizations and construction firms is conducive to the evolution of the system in a positive direction, but excessive rewards can simultaneously increase financial pressure and reduce the government’s incentive to regulate.

5. Conclusions and Recommendations

To summarize, the cost driven by interests is an important factor influencing the three-party game, but the regulating role of the government’s reward and punishment mechanism is equally important. The government is both a supervisor and a guide for environmental protection organizations and enterprises, and its supervisory mechanism has a certain degree of binding force for both parties, guiding the three parties to achieve benign interaction in the process of low-carbon construction. Increasing the government’s rewards and penalties is conducive to the stable evolution of each party towards the ideal state. However, excessive government intervention, whether in the form of severe penalties or high subsidies, is not conducive to the healthy development of the system.

In light of this, the paper proposes the following recommendations.

Establish a Robust Regulatory Framework: The government should enforce penalties for legal violations, prioritize supervision and guidance for enterprises in implementing environmental protection measures, ensure compliance with low-carbon construction regulations and standards, and safeguard ecological integrity and public interests. Additionally, it should institute incentive mechanisms such as tax breaks and financial support to reward enterprises demonstrating positive strides in low-carbon construction.

Implement Balanced Incentives and Penalties: During regulation, the government should maintain moderate incentives and penalties to foster tripartite collaboration. Excessive measures could hinder cooperative development.

Leverage Environmental Organizations’ Regulatory Role: Environmental protection entities can actively oversee and engage in supervision, utilizing environmental advocacy and public welfare initiatives to facilitate public scrutiny and social involvement. This encourages construction enterprises to better fulfill their societal obligations.

Enhancing Corporate Social Responsibility: Construction companies should follow low-carbon design standards, including the use of renewable and environmentally friendly building materials, optimizing building design, and reducing carbon emissions during construction.

Enhance Tripartite Cooperation: The government can foster collaboration between construction enterprises and environmental organizations, offering policy backing and resource allocation while encouraging joint efforts in technology research, project implementation, and other areas to advance low-carbon construction.

While this study delves into the game mechanism and its implications for the government, construction enterprises, and environmental organizations in low-carbon construction, it is essential to acknowledge the influence of other enterprises and stakeholders on carbon emission reduction in practice. Consideration could be given, for example, to the role of the public scrutiny of construction firms and governments by consumers, the media, and other members of society. The refinement of the government’s role in monitoring and incentivizing construction firms and other civic organizations can also be considered. In addition, refining the factors that influence the decision-making of the parties involved is also an important development for future research. Subsequent research can improve on these two aspects, thus providing more effective and feasible strategic guidance for realizing carbon emission reduction goals.