Promoting the Sustainable Development of Power Construction Projects through Stakeholder Participant Mechanisms: An Evolutionary Game Analysis

Abstract

The sustainable development of power construction projects (PCPs) is of great significance in solving the issue of high carbon emissions in the power industry. However, the profit-seeking nature of stakeholders’ strategic choices and other conflicts have seriously hindered this process. This study constructs a tripartite game evolution model for the government, grid companies and the public, and determines the factors and range of values that affect the behavioral and strategic choices of stakeholders based on the literature analysis method and case study method. Numerical simulations are conducted with the help of MATLAB R2021a software to explore the changes in decision-making behavior of stakeholders and system stabilization strategies in different stages of the industry life cycle and the influencing mechanisms. The results show that in the initial stage, the government lays the foundation for the development of PCPs through policy guidance under the government-led mechanism. As PCPs move into the development stage, stakeholders’ benefits increase, creating a collaborative participation situation. As PCPs mature, the role of market guidance comes to the fore, and the interventionist role of government diminishes to a guardian role. In terms of sensitivity analysis of relevant parameters, low government rewards and penalties are not conducive to the adoption of low-carbon sustainable construction programs by power grid companies. The public influences the sustainable behavior of the government and power grid companies through public opinion. In addition, reasonable cost inputs from all stakeholders are critical to effectively promote the steady growth of PCPs. Based on the results, a sustainable development promotion mechanism for PCPs is constructed based on multiple dimensions, with a view to providing decision-making services for stakeholders and thus contributing to the sustainable development of PCPs.

1. Introduction

The Annual Report on Carbon Neutrality and Clean Air in China (2021) states that the power industry in China accounts for about 41% of the total national carbon emissions, while the power industry internationally accounts for about 32% of the global carbon emissions [1]. As industrialization in China accelerates, the demand for electricity from various industries and the public is gradually increasing, and the number of power construction projects (PCPs) continues to grow [2,3]. However, the resource endowment of China determines that PCPs are still mainly based on traditional fossil fuels, causing multiple adverse impacts such as environmental pollution and climate change [4,5]. Under China’s efforts to achieve “carbon peak and carbon neutrality”, the sustainable development of PCPs is both an opportunity and a challenge [6]. Due to the imperfect government supervision mechanism of PCPs, the high cost of upfront investment by power grid companies is still unresolved, which leads to the problem of unsustainability and high carbon emissions of PCPs becoming more and more prominent [7]. However, the public has to pay for the behavior of the grid companies, which not only reduces the incentive for public participation, but also seriously affects the promotion of government policies [8,9]. As a result, the conflicts of benefits among the government, power grid companies and public have led to a dilemma in the sustainable development of PCPs.

The sustainable development of PCPs is based on the premise of promoting the application of low-carbon technological innovations and considering industrial development within the carrying capacity of resources and the environment during the life cycle of a project [10]. The benefits of stakeholders in each stage are characterized by complexity and uncertainty, so the sustainable development of PCPs is essentially a game process for the relevant stakeholders, and the state of development depends largely on the choice of behavioral strategies of each stakeholder [11]. Low-carbon behaviors are difficult for power grid companies to implement owing to the low level of low-carbon technological innovations and the high costs [12]. In addition, with the development of networking and informatization in society, convenient channels have been provided for the public to understand information related to PCPs. The public’s willingness to participate in the supervision of PCPs has become stronger and has focused public opinion on PCPs [13,14]. To avoid “market failure”, there is an urgent need for government interventions and oversight to ensure collaborative efforts [15]. Therefore, to promote the sustainable development of PCPs, it is necessary to study in depth the behavioral strategy choices of the government, power grid companies and public in different situations. However, there is a large research gap on the behavioral strategy choices of PCPs’ stakeholders. With information asymmetry and self-interest, stakeholders’ strategy choices exhibit limited rationality through multi-stage games. There is an urgent need to study the main influencing factors and the evolutionary path of the key conditions for the behavioral strategy choices of the government, power grid companies and public under the stakeholders’ participation mechanism from the perspective of combining theory and practice.

To address the actual development dilemma of PCPs and effectively safeguard the vital benefits of critical stakeholders in the process of the sustainable development of PCPs, this study aims to solve the following questions:

(1)

What are the factors that influence the behavioral strategy choices of critical stakeholders in the sustainable development of PCPs?

(2)

What are the interactions of critical stakeholders and the steady state of the system guided by different participation mechanisms in the sustainable development of PCPs?

(3)

What are the mechanisms for the sustainable development of PCPs in different development stages?

2. Literature Review

2.1. Sustainable Development of PCPs

With the gradual increase in the demand for social progress and improvement of people’s quality of life, the sustainable development of PCPs has attracted extensive attention from the academic community as a model with good development prospects. To contribute to the low-carbon sustainable development of PCPs, many scholars have carried out relevant research. Li et al. [16] took the production, transport and construction stages of PCPs as entry points to explore the sources of carbon emissions and target carbon reduction pathways to promote the sustainable development of PCPs. Ali et al. [17] evaluated the green technology strategy for the sustainable development of solar power projects and proved that the green technology strategy has a positive effect on the sustainable development of PCPs. Irfan et al. [18], based on the SWOT model with a view to help the sustainable development of PCPs through wind power, proposed important policy measures to steady the growth of the wind power industry. Xu et al. [19] established an investment risk assessment and optimization process for wind power projects in China to reduce the risk to the sustainable development of PCPs and proposed specific measures for renewable energy to help the sustainable development of PCPs. It can be found that previous scholars have mostly researched from the perspective of adopting low-carbon technologies and clean energy and have fully proven the high efficiency of low-carbon technologies and other tools [20,21]. While low-carbon technologies provide the new engine for sustainable development in PCPs, the adoption willingness of PCP stakeholders is the key to successful implementation [22]. PCP stakeholders have been hesitant to implement the low-carbon sustainable transition due to the input costs, policy environment, market environment, etc. [23]. In addition, based on the dynamic development of PCPs, the conflicts of interest and interactions between stakeholders are not yet clear, leading to the lack of current research that still exists. Therefore, on the basis of previous research, this study continues to study in depth the behavioral strategy choices of stakeholders in the sustainable development process of PCPs in a significant way, using relevant low-carbon technologies as a means to achieve this.

2.2. Critical Stakeholders in the Sustainable Development of PCPs

According to the concept of construction project stakeholder theory, the stakeholders related to the sustainable development of PCPs can be described as individuals or organizations that influence or are influenced by the decision-making activities of the project [24,25]. All stakeholders contribute to the sustainable development of PCPs. In general, PCP stakeholders include, but are not limited to, government departments, power grid companies, designers, contractors, and the public [26,27]. However, the strategy choices of stakeholders such as designers and others depend on the contract with the power grid companies [28,29]. The selection of the construction programs of the power grid companies is critical to the sustainable development of PCPs and is also an important object of governmental supervision and management [30]. The power grid companies are driven by profit-seeking objectives to maximize their own economic profits. However, the resulting unsustainable behaviors have caused environmental pollution, high carbon emissions and many other problems, which not only increase the input costs, but also damage the brand value of the power grid companies [31]. The government plays in a leading role in the sustainable development of PCPs, aiming to take into account the economic benefits brought about by the development of PCPs while at the same time taking into account the environmental and social benefits. The government imposes rewards and penalties to drive power grid companies to implement low-carbon sustainable construction programs and promotes active public participation in supervision through policy advocacy [32]. The public, as the external stakeholder of PCPs, is not directly involved in the construction process of PCPs. In the context of the era of rapid development of information technology, the channels for public participation in the management of PCPs have significantly increased. As the user group of PCPs, the public expects environmental improvements and quality of life improvements to be brought by the sustainable development of PCPs [33]. Once the public is aware of the irregularities of other stakeholders, there will be rhetorical pressure and complaints, devaluing the grid company’s brand and causing a negative impact on the government’s image [34,35]. Therefore, the government, power grid companies and public are chosen as the critical stakeholders of PCPs.

2.3. Evolutionary Game Theory

The sustainable development of PCPs is a dynamic process of change involving many different stages, in which the behavioral strategy choices of stakeholders are constantly changing. The interactions among stakeholders in different stages greatly affect the steady state of PCPs. Evolutionary game theory aims to explore the dynamic evolution of the game situation of different subjects over time [30,36]. Therefore, the application of an evolutionary game to study the change in stakeholders’ behavioral strategies in the process of the sustainable development of PCPs has good adaptability and rationality. In recent years, evolutionary game theory has been widely used to study the interaction of different stakeholders in construction projects, which in turn helps the sustainable development of the projects. Yuan et al. [37] established a tripartite evolutionary game model with the government, developers, and consumers as the main participants, and explored the evolutionary process of the system under different rewards and penalties in order to promote the sustainable development of the prefabricated building industry in China. Yang et al. [38] developed a tripartite evolutionary game model including the government, focal enterprises and public to facilitate the sustainable development of infrastructure projects by exploring the responsible innovation behaviors of stakeholders in different stages of the project and the sensitivity of the relevant parameters. Feng et al. [39], based on the government-led perspective, identified three stages of green building project development and analyzed the strategy choices of stakeholders in multiple contexts. Zhu et al. [40] established an evolutionary game model based on the key characteristics of large-scale construction projects to explore the collaboration between contractors, with a view to providing a reference for the decision making of green supply chain stakeholders in large-scale construction projects. By combing through the previous literature, it can be found that evolutionary game theory has been widely applied in the study of interactions and strategy choices among stakeholders in different stages of construction projects. Therefore, this study applies evolutionary game theory to explore the different stages of the sustainable development of PCPs, enriching the related body of knowledge.

2.4. Research Gaps

A review of the relevant literature indicates that previous scholars have adequately studied the critical stakeholders and theoretical basis for the sustainable development of PCPs, providing the inspiration and theoretical basis for this study. However, there are still some research gaps.

(1)

In terms of studies on the sustainable development of PCPs. It is important to note that the sustainability process of PCPs is dynamic and multi-stage, and the roles played by stakeholders change. However, there is still a research gap regarding the changes in the behavioral strategy choices of stakeholders at different stages of development of PCPs and the interaction mechanisms.

(2)

From the perspective of critical stakeholders in the sustainable development of PCPs. In the context of the new era and new challenges, the mechanisms for stakeholder participation are changing. It is worth noting that the role of public influence has become increasingly prominent. Therefore, there is an urgent need for a comprehensive study of PCPs under market-led and collaboration participant mechanisms.

(3)

Regarding the research methodology. Evolutionary game theory provides ideas for research that addresses the sustainability of construction projects. However, studies exploring the impact of different factor changes on the behavioral strategies of stakeholders mostly focus on a certain stage or subject. PCPs are multi-party collaborative projects that need to be assessed based on parametric sensitivity analysis from a multi-participant, multi-stage perspective.

3. Materials and Methods

3.1. Model Assumptions

The industry life cycle theory points out that an industry, from its emergence until the complete withdrawal of its socio-economic activities, mainly includes four stages of development: infancy, growth, maturity, and decline [41,42]. According to the characteristics of the critical stakeholders and development of PCPs, this study constructed the logical relationship of the main participants of the sustainable development of PCPs, as shown in Figure 1, which depicts the interaction of critical stakeholders in the sustainable development process of PCPs under the government-led, collaborative participation and market-led mechanisms.

This study proposed the following research assumptions:

Assumption 1.

The evolutionary game model includes the government, power grid companies, and the public. All three are limited rational participants, can make independent decisions, and the behavioral strategy choices are stable according to the optimal strategy with time evolution.

Assumption 2.

The behavioral strategy choices of the government include rigorous supervision (RS) and lax supervision (LS). The rigorous supervision strategy implies that the government rigorously reviews the implementation of low-carbon construction programs by power grid companies during the PCP implementation process [15]. The government will provide incentives such as policy subsidies to power grid companies that meet low-carbon construction standards [43]. At the same time, the government will also impose penalties on power grid companies that fail to meet low-carbon construction standards [44]. In addition, the government’s rigorous supervision behavior enhances the credibility and provides the public with the assurance of access to information [32]. In contrast, lax supervision indicates that the government does not establish substantial incentives due to information asymmetry.

Assumption 3.

The behavioral strategy choices of the power companies include adopting low-carbon construction programs (LCP) and traditional construction programs (TCP). The power grid companies may adopt low-carbon construction programs and pay additional construction costs based on sustainability and government incentives [7,12]. Low-carbon construction programs implemented by power grid companies also bring environmental benefits to the government and public [16]. Meanwhile, power grid companies may also adopt traditional construction programs with a focus on short-term benefits, which will have a negative impact on the environment [45].

Assumption 4.

The behavioral strategy choices of the public include positive participation (PP) and negative participation (NP). Active public participation will result in the opportunity cost of obtaining relevant information, and there will be positive feedback on the government’s rigorous supervision and power companies’ low-carbon construction behavior [16,46]. In contrast, negative participation means that the public will not take the initiative to obtain relevant information and will find it difficult to give timely feedback [47].

Assumption 5.

For the aspect of strategy adoption probability, the probabilities that the government, power grid companies and public choose strict supervision, low-carbon construction programs and positive participation are x (0 ≤ x ≤ 1), y (0 ≤ y ≤ 1), and z (0 ≤ z ≤ 1), respectively. The probabilities of choosing lax supervision, traditional construction programs, and negative participation are (1 − x), (1 − y), and (1 − z), respectively.

The government, power grid companies and public all have their own behavioral strategy choices and benefits. The behavioral strategy choices of any one stakeholder affect and are affected by the other two. Different behavioral strategy choices have different impacts on PCPs, in a dynamic process. This study searched the WOS database for the relevant literature with the following keywords: power construction projects AND (power industry or grid projects or electricity construction projects) AND (sustainability or uncertainty or challenges) AND (stakeholders or government or power grid companies or public).

Table 1. Descriptions of relevant parameters.

Parameters	Descriptions	References
C1	Input costs for the Government to implement rigorous supervision strategies.	[7,48]
B1	Benefits for the Government to implement rigorous supervision strategies.
S	Government subsidies for power grid companies to select low-carbon construction programs.	[43,44]
P	Government-imposed penalties for power grid companies failing to fulfil low-carbon mandates.	[15,44]
L	Loss of credibility resulting from government’s lax supervision strategies when the public actively participates.	[13]
G	Cost of environmental governance to government when power grid companies fail to fulfil low-carbon mandates.	[15,45]
C2	Input costs for power grid companies to implement traditional construction programs.	[49]
B2	Benefits for power grid companies implementing traditional construction programs.
C3	Input extra costs for power grid companies to implement low-carbon construction programs.	[7,12,48]
B3	Extra benefits for power grid companies implementing low-carbon construction programs.
E1	Environmental benefits to government when power grid companies implement low-carbon construction programs.	[45]
V	Value-added branding generated by power grid companies implementing low-carbon construction programs.	[9,14]
D	Devaluation of the brand image caused by the failure of power grid companies to fulfil low-carbon mandates.
C4	Opportunity costs of public positive participation in PCPs.	[35,47]
B4	Benefits from positive public participation in PCPs.
E2	Extra benefits to the public when low carbon policy measures are adopted by both government and power grid companies.	[16,46]
I	The loss to the public of the failure of power grid companies to fulfil low-carbon mandates.	[4,16,50]

demonstrates the relevant parameters that influence the benefits and costs of the three stakeholders under different behavioral strategy choices.

Based on the above assumptions, this study constructed a tripartite game payoff matrix based on the different strategy choices of the government, power grid companies and public, as shown in

Table 2. Stakeholder benefits matrix.

Strategy Choice	Government	Power Grid Company	Public
(RS, LCP, PP)	−C1 + B1 − S + E1	−C2 − C3 + B2 + B3 + S + V	−C4 + B4 + E2
(RS, LCP, NP)	−C1 + B1 − S + E1	−C2 − C3 + B2 + B3 + S + V	0
(LS, LCP, PP)	E1 − L	−C2 − C3 + B2 + B3 + V	−C4 + B4
(LS, LCP, NP)	E1	−C2 − C3 + B2 + B3 + V	0
(RS, TCP, PP)	−C1 + B1 + P − G	−C2 + B2 − P − D	−C4 + B4 − I
(RS, TCP, NP)	−C1 + B1 + P − G	−C2 + B2 − P	−I
(LS, TCP, PP)	−G − L	−C2 + B2 − D	−C4 + B4 − I
(LS, TCP, NP)	−G	−C2 + B2	−I

. In addition, for the value range of each parameter in Table 2, the values were determined by combining expert opinions and case studies. This study was based on the project cases provided by the State Grid Liaoning Electric Power Company Limited, Economic Research Institute and in-depth exchanges with experts in the power industry.

3.2. Model Establishment

According to Table 2, this study calculated the expected benefits and average expected benefits of different stakeholders choosing different behavioral strategies. Firstly, this study calculated the expected benefits of the government’s choice of the RS strategy and the LS strategy, indicated by E_x and E_1−x, respectively, and the average expected benefit is indicated by $\overline{E_x}$.

E_x = yz(−C₁ + B₁ − S + E₁) + y(1 − z)(−C₁ + B₁ − S + E₁) + (1 − y)z(−C₁ + B₁ + P − G) + (1 − y)(1 − z)(−C₁ + B₁ + P − G) = y(E₁ + G − S − P) − C₁ + B₁ + P − G

(1)

E_1−x = yz(E₁ − L) + y(1 − z)E₁ + (1 − y)z(−G − L) + (1 − y)(1 − z)(−G) = y(E₁ + G) − zL − G

(2)

$$\overline{{\mathrm{E}}_{\mathrm{x}}}=\mathrm{x}{\mathrm{E}}_{\mathrm{x}}+(1-\mathrm{x}){\mathrm{E}}_{1-\mathrm{x}}$$

(3)

Based on Equations (1)–(3), this study obtained the replication dynamic equation for the government’s implementation of the RS strategy as in Equation (4):

$$\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{dx}}{\mathrm{dt}}=\mathrm{x}({\mathrm{E}}_{\mathrm{x}}-\overline{{\mathrm{E}}_{\mathrm{x}}})=\mathrm{x}(1-\mathrm{x})(-\mathrm{y}(\mathrm{S}+\mathrm{P})+\mathrm{zL}-{\mathrm{C}}_1+{\mathrm{B}}_1+\mathrm{P})$$

(4)

Secondly, this study calculated the expected benefits of the LCP and TCP strategies chosen by the power grid companies, indicated by E_y and E_1−y, respectively, and the average expected benefit is indicated by $\overline{E_y}$.

E_y = xz(−C₂ −C₃ + B₂ + B₃ + S + V) + x(1 − z)(−C₂ −C₃ + B₂ + B₃ + S + V) + (1 − x)z(−C₂ −C₃ + B₂ + B₃ + V) + (1 − x)(1 − z)(−C₂ − C₃ + B₂ + B₃ + V) = xS − C₂ −C₃ + B₂ + B₃ + V

(5)

E_1−y = xz(−C₂ + B₂ − P − D) + x(1 − z)(−C₂ + B₂ − P) + (1 − x)z(−C₂ + B₂ − D) + (1 − x)(1 − z)(−C₂ + B₂)
= −xP − zD − C₂ + B₂

(6)

$$\overline{{\mathrm{E}}_{\mathrm{y}}}=\mathrm{y}{\mathrm{E}}_{\mathrm{y}}+(1-\mathrm{y}){\mathrm{E}}_{1-\mathrm{y}}$$

(7)

Based on Equations (5)–(7), this study obtained the replication dynamic equation for the implementation of the RS strategy by power grid companies as in Equation (8):

$$\mathrm{F}(\mathrm{y})=\frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{y}({\mathrm{E}}_{\mathrm{y}}-\overline{{\mathrm{E}}_{\mathrm{y}}})=\mathrm{y}(1-\mathrm{y})(\mathrm{x}(\mathrm{S}+\mathrm{P})+\mathrm{z}\mathrm{D}-{\mathrm{C}}_3+{\mathrm{B}}_3)$$

(8)

Finally, the study calculated the expected benefits of the PP and NP strategies chosen by the public, indicated by E_z and E_1−z, respectively, and the average expected benefit is indicated by $\overline{E_z}$.

E_z = xy(−C₄ + B₄ + E₂) + x(1 − y)(−C₄ + B₄ − I) + (1 − x)y(−C₄ + B₄) + (1 − x)(1 − y)(−C₄ + B₄ − I)
= xyE₂ + yI − C₄ + B₄ − I)

(9)

E_1−z = x(1 − y)(−I) + (1 − x)(1 − y)(−I)= (1 − y)(−I)

(10)

$$\overline{{\mathrm{E}}_{\mathrm{z}}}=\mathrm{z}{\mathrm{E}}_{\mathrm{z}}+(1-\mathrm{z}){\mathrm{E}}_{1-\mathrm{z}}$$

(11)

Based on Equations (9)–(11), this study obtained the replication dynamic equation for the public implementation of PP strategy as in Equation (12):

$$\mathrm{F}\left(\mathrm{z}\right)=\frac{\mathrm{dz}}{\mathrm{dt}}=\mathrm{z}({\mathrm{E}}_{\mathrm{z}}-\overline{{\mathrm{E}}_{\mathrm{z}}})=\mathrm{z}(1-\mathrm{z})({\mathrm{xyE}}_2-{\mathrm{C}}_4+{\mathrm{B}}_4)$$

(12)

Combining Equations (4), (8) and (12), this study constructed a three-dimensional dynamic system, which in turn calculated the equilibrium point of the tripartite evolutionary game.

$$\left\{\begin{array}{c}\mathrm{F}(\mathrm{x})=\frac{\mathrm{dx}}{\mathrm{dt}}=\mathrm{x}({\mathrm{E}}_{\mathrm{x}}-\overline{{\mathrm{E}}_{\mathrm{x}}})=\mathrm{x}(1-\mathrm{x})(-\mathrm{y}(\mathrm{S}+\mathrm{P})+\mathrm{z}\mathrm{L}-{\mathrm{C}}_1+{\mathrm{B}}_1+\mathrm{P})\\ \mathrm{F}(\mathrm{y})=\frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{y}({\mathrm{E}}_{\mathrm{y}}-\overline{{\mathrm{E}}_{\mathrm{y}}})=\mathrm{y}(1-\mathrm{y})(\mathrm{x}(\mathrm{S}+\mathrm{P})+\mathrm{z}\mathrm{D}-{\mathrm{C}}_3+{\mathrm{B}}_3)\\ \mathrm{F}(\mathrm{z})=\frac{\mathrm{dz}}{\mathrm{dt}}=\mathrm{z}({\mathrm{E}}_{\mathrm{z}}-\overline{{\mathrm{E}}_{\mathrm{z}}})=\mathrm{z}(1-\mathrm{z})({\mathrm{xyE}}_2-{\mathrm{C}}_4+{\mathrm{B}}_4)\end{array}\right.$$

(13)

Based on Equation (13), when F(x) = 0, F(y) = 0, and F(z) = 0, eight pure strategy equilibrium points of the system could be identified: e₁(0,0,0), e₂(0,0,1), e₃(0,1,0), e₄(1,0,0), e₅(0,1,1), e₆(1,0,1), e₇(1,1,0), e₈(1,1,1), and the mixed strategy equilibrium point e*(x*, y*, z*), as shown in Equation (14).

$$\left\{\begin{array}{c}-\mathrm{y}(\mathrm{S}+\mathrm{P})+\mathrm{z}\mathrm{L}-{\mathrm{C}}_1+{\mathrm{B}}_1+\mathrm{P}=0\\ \mathrm{x}(\mathrm{S}+\mathrm{P})+\mathrm{z}\mathrm{D}-{\mathrm{C}}_3+{\mathrm{B}}_3=0\\ {\mathrm{xyE}}_2-{\mathrm{C}}_4+{\mathrm{B}}_4=0\end{array}\right.$$

(14)

3.3. Analysis of ESS

It is uncertain whether the nine equilibrium points in the system are evolutionary stable strategies (ESS). Previous studies have shown that the equilibrium point in a system of replicated dynamic equations of an evolutionary game is ESS only if the asymptotically stable equilibrium point satisfies both the strict Nash equilibrium and the pure strategy Nash equilibrium. In the tripartite evolutionary game system constructed in this study, e*(x*, y*, z*) does not satisfy the requirements as a mixed-strategy equilibrium point. Therefore, it was not considered. This study verified the asymptotic stability of these equilibrium points by analyzing the eigenvalues of the Jacobi matrix of the system. According to the Lyapunov stability theory [51], the following criterion on the Jacobi matrix can be used to determine whether the Nash equilibrium point is an ESS or not, i.e., a sufficient condition for satisfying an ESS is that all eigenvalues of the Jacobi matrix of the system are negative. Based on Equation (13), this study obtained the Jacobi matrix as follows:

$$\mathrm{J}=\left[\begin{array}{ccc}\frac{\partial F\left(x\right)}{\partial x}& \frac{\partial F\left(x\right)}{\partial y}& \frac{\partial F\left(x\right)}{\partial z}\\ \frac{\partial F\left(y\right)}{\partial x}& \frac{\partial F\left(y\right)}{\partial y}& \frac{\partial F\left(y\right)}{\partial z}\\ \frac{\partial F\left(z\right)}{\partial x}& \frac{\partial F\left(z\right)}{\partial y}& \frac{\partial F\left(z\right)}{\partial z}\end{array}\right]=\left[\begin{array}{ccc}{J}_{11}& J_{12}& J_{13}\\ J_{21}& J_{22}& J_{23}\\ J_{31}& J_{32}& J_{33}\end{array}\right]$$

(15)

Among them, J₁₁ = (1 − 2x)[zL − y(S + P) − C₁ + B₁ + P], J₁₂ = x(1 − x)(−S − P), J₁₃ = x(1 − x)L, J₂₁ = y(1 − y)(S + P), J₂₂ = (1 − 2y)(x(S + P) − C₃ + B₃ + V + zD), J₂₃ = y(1 − y)D, J₃₁ = z(1 − z)y E₂, J₃₂ = z(1 − z)xE₂, J₃₃ = (1 − 2z)(xyE₂ − C₄ + B₄). Subsequently,

Table 3. Stable conditions for equilibrium points.

Equilibrium Points	Eigenvalues			Conditions
	λ1	λ2	λ3
e1(0, 0, 0)	B1 − C1 + P	B3 − C3	B4 − C4	λ1 < 0, λ2 < 0, λ3 < 0
e2(1, 0, 0)	−B1 + C1 − P	B3 − C3 + P + S	B4 − C4	λ1 < 0, λ2 < 0, λ3 < 0
e3(0, 1, 0)	B1 − C1 − S	C3 − B3	B4 − C4	λ1 < 0, λ2 < 0, λ3 < 0
e4(0, 0, 1)	B1 − C1 + L + P	B3 − C3 + D	C4 − B4	λ1 < 0, λ2 < 0, λ3 < 0
e5(1, 1, 0)	C1 − B1 + S	C3 − B3 − P − S	B4 − C4 + E2	λ1 < 0, λ2 < 0, λ3 < 0
e6(0, 1, 1)	B1 − C1 + L − S	C3 − B3 − D	C4 − B4	λ1 < 0, λ2 < 0, λ3 < 0
e7(1, 0, 1)	C1 − B1 − L − P	C3 − B3 + D + P + S	C4 − B4	λ1 < 0, λ2 < 0, λ3 < 0
e8(1, 1, 1)	C1 − B1 − L + S	C3 − B3 − D − P − S	C4 − B4 − E2	λ1 < 0, λ2 < 0, λ3 < 0

shows the eigenvalues of all equilibrium points calculated in this study and the corresponding conditions under which they satisfy the ESS of the system.

Due to space constraints and the actual development of PCPs, the full ESS could not be analyzed in this study. Combined with the industry life cycle, this study further developed the perspective of the PCP industry to ensure the stability of the system, as shown in Figure 2, dividing the life cycle of PCPs into the initial stage, the development stage, and the mature stage, and choosing the ESS corresponding to these three stages. In the initial stages of PCPs, the system ESS corresponds to e₂(1, 0, 0) and the tripartite behavioral strategy choices are (RS, TCP, NP). An urgent need exists for low-carbon sustainable development in PCPs and the government is facing enormous pressure from environmentally friendly development. In this situation, the government will take the initiative to implement the RS strategy to confirm the dominant role and lay the foundations for the development of PCPs. The inequality C₁ < B₁ + P suggests that the benefits of the government’s RS strategy outweigh the input costs. While in the initial stage of PCPs, the benefits of implementing LCP by the power grid companies are not significant, the inequality B₃ + P + S < C₃ further proves that the power companies prefer to accept the penalty and choose the TCP strategy. According to the inequality B₄ < C₄, the public positively participates in obtaining benefits that are lower than the costs, and the public will choose the NP strategy.

With the improvement of government policies and related standards, PCPs will gradually enter the development stage, and public participation in PCP supervision will be much greater. Driven by both public supervision and policy improvements, power gird companies tend to choose the LCP strategy. Therefore, the government, power grid companies and public collaborate with the system ESS corresponding to e₈(1, 1, 1), and the tripartite behavioral strategy choices are (RS, LCP, PP), where the inequality C₁ + S < B₁ + L suggests that the decline in credibility due to the choice of LS by the government during the development stage cannot be ignored. In addition, besides providing financial subsidies to the power grid companies, etc., the benefits from implementing the RS strategy by the government outweigh the costs, and it continues to promote the low-carbon development policy. From the inequality C₃ < B₃ + D + P + S, it can be found that the power grid companies’ choice of TCP strategy will incur negative public evaluation and lead to a decline in their own brand value. The power grid companies implement LCP strategies to gain government and public support and achieve low-carbon development benefits over costs. The inequality C₄ + I < B₄ + E₂ suggests that the public positively participates in PCP supervision to protect their own interests and that the benefits of implementing the PP strategy are higher than the input costs.

As PCPs steadily develop into a fully sustainable system, the government will gradually withdraw from the market and power grid companies will still need to positively adopt low-carbon operations and maintenance. The public becomes the main user, influencing the power grid companies through public opinion. The system ESS corresponds to e₆(0, 1, 1) and the tripartite behavioral strategy choices are (LS, LCP, PP). The inequality B₁ + L < C₁ + S confirms that the benefits of the government RS strategy are lower than the costs. The inequality C₃ < B₃ + D indicates that the benefits of implementing the LCP strategy by the grid company are higher than the costs. According to the inequality C₄ + I < B₄, the public will choose to positively participate in the supervision and management of PCPs when the benefits received from the implementation of the PP strategy are greater than the costs.

4. Numerical Simulations

In the theoretical analysis, this study identified the corresponding conditions for stakeholders’ behavioral strategy choices. To visualize the evolution of ESS at different stages, this study performed numerical simulations with the help of MATLAB 2021a software to analyze the changes in the trajectory of stakeholders’ behavioral evolution. In addition, to ensure that the parameters are set scientifically and reasonably, this study combined actual cases of PCPs, such as the Liaoning Tianrun Kaiyuan City Zhongguo Town Wind Power Project 66 KV Transmission Project, the Shenyang Offshore 220 KV Transmission Project, and the Liaoning Yong’an 500 KV Transmission Project, and other PCPs with different voltage levels and scales and engaged in discussions with experts from the State Grid Liaoning Institute of Economics and Technology. At the same time, the public around the project was fully investigated regarding their willingness and demand, so as to reasonably set the value for the parameters of the different stages, as shown in

Table 4. Values of parameters in different stages.

Parameters	C1	B1	S	P	L	G	C2	B2	C3	B3	E1	V	D	C4	B4	E2	I
Initial Stage	12	20	6	3	3	4	10	15	20	6	5	4	3	8	3	4	2
Development Stage	12	20	8	3	4	4	10	15	10	6	5	4	4	6	9	5	2
Mature Stage	12	10	7	3	3	4	10	15	5	6	5	4	4	4	12	5	2

.

4.1. Dynamic Evolutionary Trajectories and Parameter Sensitivity Analysis in the Initial Stage

4.1.1. Dynamic Evolutionary Trajectories in the Initial Stage

In this study, numerical simulations were carried out using MATLAB R2021a to ensure that the values of the parameters corresponding to the initial stage satisfy the conditions in Figure 2 regarding the stability conditions, i.e., C₁ < B₁ + P, B₃ + P + S < C₃, B₄ < C₄. Then, 100 sets of different initial strategy points for x, y, and z were randomly generated, and the different colored lines show the trajectories of the tripartite evolutionary game with 100 randomly generated unfixed initial strategies provided by the MATLAB R2021a software, verifying that the equilibrium point e₂(1,0,0) is an ESS in the system, as shown in Figure 3a. Further, this shows that the behavioral choice strategies of the government, power grid companies and public are (RS, TCP, PP) under the satisfaction of the initial stage constraints. Specifically, in the initial stage of PCPs, the government, as the leader, will facilitate PCPs to meet sustainable development needs. However, factors such as low-carbon construction costs for power grid companies and weak environmental awareness influence the sustainable transformation of PCPs. In addition, the high cost of public participation in PCP supervision and the lack of knowledge about the low-carbon construction of PCPs make the willingness to positively participate less strong.

As shown in Figure 3b, the behavioral strategy choice probabilities of the government, power grid companies and public eventually converge to ESS(1,0,0) over time. The government implements the RS strategy to reach a stable state as fast as possible. The public chooses the NP strategy to reach the stable state at the slowest rate. Compared to the public, power grid companies implement TCP strategies to reach a stable state slightly faster. In the initial stage of PCPs, faced with the enormous pressure of low-carbon transformation of PCPs, the government plays a role in policy promotion to lay the foundations for the sustainable development of PCPs. The power grid companies are driven by their own benefits, and with the initial implementation of relevant policies, the policy system is not yet perfect, meaning that the willingness of power grid companies to implement low-carbon construction programs is low. Therefore, relevant stakeholders need to be encouraged to change their strategy choices over time.

4.1.2. Parameter Sensitivity Analysis in the Initial Stage

Since the government is the main player in the initial stage of PCPs, it is necessary to explore the impact of changes in government-related parameters on the behavioral strategy choices of other stakeholders. In this study, government policy incentives, including subsidies S, penalties P, and rigorous supervision costs C₁, are chosen for numerical simulation sensitivity analysis. Firstly, this study set S as 6, 12, and 18, and the results of sensitivity analysis are shown in Figure 4. Figure 4a shows the impact of the government implementing the RS strategy when S changes. When S takes values of 6 and 12, the government still chooses to implement the RS strategy. S gradually increases to 18, exceeding the constraints of the stable state of the system in the initial stage, and the probability of the government implementing the RS strategy decreases significantly, and the behavioral strategy choice gradually prefers the LS strategy. For the government, the additional social benefits arising from the implementation of the RS strategy in the initial stage of PCPs are not obvious, and excessive policy incentives will put greater financial pressure on the government, preventing the implementation of the RS strategy. Figure 4b shows the corresponding changes in the behavioral strategy choices of the power grid companies in the case of S changes. It is clear that government incentives have a positive impact on the implementation of the LCP strategy by power grid companies. The probability that power grid companies will implement the LCP strategy increases gradually with increasing S.

This study explores the changes in the behavioral strategy choices of the government and power grid companies in the case of P changes in the initial stage. This study sets P as 3, 6, and 9 and the results of sensitivity analysis are shown in Figure 5. In particular, Figure 5a illustrates the impact of P on the government. It can be found that the probability of the government implementing the RS strategy increases as the P increases. Higher penalties generate additional revenue for the government and increase the probability of the RS strategy. Figure 5b illustrates the change in behavioral strategy choices when power grid companies are under different levels of penalties. When P is 3, the power grid companies implement the TCP strategy. As P continues to increase, the probability that the power grid companies will choose the LCP strategy improves. Specifically, lower P does not contribute to the implementation of the LCP strategy for power grid companies. In contrast, the pressure on grid companies gradually increases with increasing P, which has a facilitating impact on the low-carbon transition of power grid companies.

Finally, to understand how the supervision costs C₁ impacts on the behavioral strategy choices of the government, this study set C₁ as 12, 22, and 32. The numerical simulation is shown in Figure 6. The government chooses to implement the RS strategy when the value of C₁ is 12. As C₁ continues to increase, the probability of the government choosing the RS strategy decreases, and it eventually changes to practicing the LS strategy. Thus, the government tends to choose the RS strategy when C₁ is low and the rate of evolution is accelerating. Specifically, the implementation of the RS strategy by the government requires higher supervision costs, but these high supervision costs will reduce the government’s willingness to supervise. In the initial stage of PCPs, the participation of the power companies and public is low, and the understanding of government policies needs to be improved. Therefore, the government needs to consider the rationality of supervision costs, otherwise it will impact the behavioral strategy choices of other stakeholders in the subsequent stages, preventing the system from reaching a stable state.

4.2. Dynamic Evolutionary Trajectories and Parameter Sensitivity Analysis in the Development Stage of PCP

4.2.1. Dynamic Evolutionary Trajectories in the Development Stage

Numerical simulations were performed according to the constraints of the PCP development stages in Figure 2, i.e., C₁ + S < B₁ + L, C₃ < B₃ + D + P + S, C₄ < B₄ + E₂. The simulation results of the 100 sets of randomly generated initial strategy points for x, y, and z are shown in Figure 7a. Different colored lines representing the trajectories of the tripartite evolutionary game finally converge at e₈(1, 1, 1). During the development stage of PCPs, government rewards and penalties gradually improve, and the promotion of low-carbon sustainable transformation for grid companies gradually increases. The channels for the public to obtain information about the construction of PCPs are more extensive, which also provides the platform for the public to express their own opinion and ideas. As a result, the public pressure further pushes the grid companies to implement the LCP strategy. The channels for the public to obtain information about the construction of PCPs are more extensive, which also provides the platform to express their own opinion. As a result, the public pressure further pushes the power grid companies to implement the LCP strategy.

The process of the government, power grid companies, and public reaching the stable state of the system is shown in Figure 7b. Over time, all three behavioral strategy choices eventually converge to e₈(1, 1, 1). The grid companies provide the fastest rate of reaching the stable state by implementing the LCP strategy. The rate at which the public implements the PP strategy to reach a stable state is the slowest. In the development stage of PCPs, grid companies are driven by both the government and public, so they reach the stable state as fast as possible. There is a good practical basis for the government to implement the RS strategy in the development stage of PCPs. In addition, the positive participation of the public also has significant impacts on the government’s credibility and further eases the pressure on the government’s supervision costs. The low-carbon measures taken by the government and power grid companies provide additional economic and social benefits to the public.

4.2.2. Parameter Sensitivity Analysis in the Development Stage

Compared to the initial stage, the impact of the parameters related to the power grid companies and public in the development stage plays an important role in the system’s stability. The parameters chosen in this study mainly included the loss of credibility L due to the government’s implementation of the LS strategy in the case of active public participation, the benefits E₂ to the public from the power grid companies’ LCP strategy and the government’s RS strategy, and the extra costs C₃ to the power grid companies of implementing the LCP strategy.

This study set L to the value of 5, 10, and 15, and the change in government behavioral strategy choices under the changing L is shown in Figure 8. Obviously, the probability of the government implementing the RS strategy increases as L continues to increase. The implementation of the government’s sustainable development policy for PCPs aims to promote quality development of the power industry, which ultimately contributes to the public’s health and well-being. As the protector of the public’s vital benefits, the government pays particular attention to the influence of public opinion, and its behavioral strategy choices are greatly impacted by the public.

The benefits to the public from the implementation of sustainable strategies by both the power grid companies and government have significant impacts on public participation. This study set E₂ to the value of 1, 5, and 9, and the results of sensitivity analysis are shown in Figure 9, which shows the changes in the public’s behavioral strategy choices with E₂. It can be found that the public’s choice of the PP strategy fails to achieve a stable state when E₂ is 1. When E₂ is 5 and 9, the evolutionary rate of the public implementing the PP strategy accelerates and the probability stabilizes at 1. At a lower E₂, the implementation of sustainable strategies by both the power grid companies and government has a weaker impact on the promotion of positive public participation. As E₂ increases, the public tends to choose PP strategies due to increased benefits. Therefore, in the development stage, the three parties promote and collaborate with each other, and ultimately promote the system to reach the optimal stable state.

Compared to traditional construction programs, there are additional costs for the power grid companies to implement low-carbon construction programs. It is necessary to analyze the impact of C₃ on the power grid companies. In this study, C₃ was set as 5, 15, and 25, and the change in the behavioral strategy choices of the power grid companies are shown in Figure 10. When C₃ is 5, the power grid companies tend to choose the LCP strategy. As C₃ gradually increases to 25, the power grid companies begin to choose the TCP strategy. Specifically, the power grid companies’ willingness to implement the LCP strategy is stronger when the additional costs are lower. When the power grid companies cannot afford the required costs of the LCP strategy, they will choose the TCP strategy.

4.3. Dynamic Evolutionary Trajectories and Parameter Sensitivity Analysis in the Mature Stage

4.3.1. Dynamic Evolutionary Trajectories in the Mature Stage

Numerical simulations are performed based on the constraints in the table for the mature stage of PCPs, i.e., B₁ + L < C₁ + S, C₃ < B₃ + D, C₄ + I < B₄. As shown in Figure 11a, this study randomly generates 100 sets of different initial strategy points of x, y, and z with the help of MATLAB R2021a software, which shows the trajectory of the three-party evolutionary game with 100 unfixed initial strategies, and further verifies that e₆(0, 1, 1) is an ESS of the system. At this time, the behavioral strategy choices of the government, the grid companies and the public are (LS, LCP, PP).

4.3.2. Parameter Sensitivity Analysis in the Mature Stage

In the maturity stage of PCPs, it is necessary to explore the impact of changes in parameters related to the power grid companies and the public. Therefore, this study chose the brand depreciation D due to the power grid companies’ failure to implement low-carbon construction and the costs C₄ required for the public to positively participate in PCPs to conduct the parameter sensitivity analyses. The value of D was set to 4, 8, and 12, and the changes in the behavioral strategy choices of the power grid companies with D are shown in Figure 12. With the value of D gradually increasing from 4 to 18, the rate of the power grid companies choosing the LCP strategy gradually accelerates and the probability stabilizes at 1. Obviously, the probability of the power grid companies implementing the LCP strategy increases with D increasing. After the previous development, the power grid companies already have strong environmental awareness and social responsibility, and will fully consider the sustainability of the project. As the government’s influence decreases, public concern about the state of development of PCPs continues to rise, which in turn impacts the brand value of power grid companies.

From the perspective of public participation, this study set C₄ as 6, 12, and 18. The changes in public behavioral strategy choices are shown in Figure 13. It can be found that the public chooses to implement the PP strategy with a probability stabilized at 1 when C₄ takes the value of 6. When C₄ gradually increases to 18, the public’s behavioral strategy choices gradually tend to favor the NP strategy. In particular, in the mature stage of PCPs, the public positively participates in the supervision of PCPs to ensure their own benefits, and they need to invest their efforts, time and other costs to understand the relevant information and express their own opinions. However, the degree of public participation is limited, and the high input costs will reduce the public’s willingness to implement the PP strategy. Broadening the sources of information available to the public and enhancing the quality of information available are key ways to promote public positive participation in project supervision.

5. Discussion

Sustainable Development Mechanism for PCPs

Driven by benefits and responsibility awareness, stakeholders’ behavioral strategy choices will change, thus impacting the process of sustainability transformation of PCPs [11,13]. This study explores the conditions under which PCPs achieve optimal solutions in different stages, as well as the sensitivity analysis of the relevant parameters, from the perspective of the project life cycle. Based on the above analysis, this study proposes a sustainable development mechanism for PCPs, as shown in Figure 14. The x-axis indicates the life cycle of PCPs, the y-axis indicates the stakeholders’ participation, and the z-axis indicates the strategies to improve the sustainability level of PCPs. With the maturity of PCPs, the comprehensive benefits brought about by the sustainable development of PCPs are gradually increasing. Due to different social responsibility and benefits, stakeholders play different roles in different stages.

In the initial stage, the additional costs for power grid companies to implement LCP strategies are higher, and public participation in understanding the progress of PCP construction is more difficult. It is worth noting that the reasons for government dominance in the initial stage of PCPs are different from other studies that focus only on the implementation of government policies [22,30]. PCPs have significant impacts on the national economy and people’s well-being. Therefore, driven by both social responsibility and economic development, the government has become the leader in the initial stage. Power grid companies face large cost burdens in adopting low-carbon sustainable programs because the economic benefits are not significant. The government should provide financial subsidies, tax exemptions and special funding to power grid companies to fully activate their enthusiasm for PCPs. At the same time, the government should also bring into play the mandatory nature of relevant laws and regulations. For power grid companies that fail to properly fulfill their carbon emission reduction responsibilities and cause environmental pollution by the overconsumption of resources and energy, the government should levy environmental pollution penalties to restrain the polluting behavior of power grid companies. In the face of the huge amount of information, the public needs to invest more time and effort to identify them, which may affect the motivation of public participation. The government needs to strengthen policy publicity to make it easier for the public to understand the information and express their opinions, so as to increase the public’s willingness to participate in project supervision.

In the development stage of PCPs, with the gradual improvement of government policies and the enhancement of social responsibility awareness of all parties, PCPs usher in a period of rapid development under collaborative cooperation. It is important for the power grid companies to effectively reduce the incremental costs of implementing low-carbon construction programs. Reducing the incremental costs requires the introduction of new materials and equipment, covering the whole industrial chain operation. Relying only on the efforts of the power grid companies is difficult to realize, and this process thus requires the positive participation of the government and public. The government strongly supports relevant R&D units to promote innovation regarding low-carbon technologies by realizing the optimal allocation of market resources and provides continuous policy subsidies for power grid companies to alleviate the cost pressure. For their own benefits and environmental awareness, the public not only understands the project construction of power grid companies, but also pays deeper attention to the progress of the implementation of government policies, thus enhancing the social image of the government and power grid companies. This leads to the increased revenue of the power grid companies, which brings environmental benefits to the government and encourages the government to establish relevant policies. The responsible behaviors of the government and power grid companies also provide reliable protection for the public benefits. A series of chain reactions create positive impacts and promote the formation of a tripartite win–win situation.

In the mature stage, PCPs develop economies of scale. In contrast to the results of other studies on the government remaining active after the sustainability of construction projects has reached a mature stage, the influence of the government in PCPs gradually decreases [38,52]. Both the power grid companies and the public, as the main participants, receive significant benefits. Real-time public supervision contributes to the sustainable transformation of power grid companies. However, public participation is limited, and once the input cost is too high, it is also not conducive to public participation. For the government, with the gradual improvement of the PCP market, the mechanism gradually changes from being government-led to being market-led. This does not mean that the government is not involved in supervision and management at all. The government should continue to focus on the direction of the future development of PCPs to avoid speculative behaviors by companies for personal gain.

6. Conclusions

This study investigates the relevant influencing factors impacting the behavioral strategy choices of stakeholders from the perspective of stakeholder participation and clarifies the evolutionary stability strategy of the system by calculating the replication dynamics equation. Secondly, combined with the project life cycle theory, this study discusses the behavioral strategy choices and interactions of stakeholders in the initial, development and mature stages of PCPs under the government-led mechanism, collaborative participation mechanism and market-led mechanism, respectively. Finally, the numerical simulation is carried out using MATLAB R2021a software to analyze the impact of different parameter variations on the evolution of stakeholders’ behavioral strategies. Specifically, the conclusions of this study are as follows.

Firstly, the critical stakeholders of PCPs play different roles guided by different mechanisms. Under the government-led mechanism, facing the dilemma that PCPs are in urgent need of low-carbon sustainable transformation, the government actively plays a leading role in constructing a favorable policy environment for the subsequent development of PCPs. Driven by benefits, the power grid companies have a lower willingness to participate in the sustainable development of PCPs from a short-term cost perspective. Similarly, the public has limited access to information resources and is not strongly interested in participation. During the development stage, with the improvement of the policy system, the benefits of stakeholders are satisfied. The development of PCPs evolves into a collaborative effort among stakeholders, supervising each other. In the mature stage, government intervention gradually decreases and the development of PCPs transforms into being market-led. The role of the public as end-users and beneficiaries gradually increases. With the mature application of low-carbon technologies, the comprehensive benefits of low-carbon sustainable development in this stage of the power grid companies are becoming more and more significant.

Secondly, different parameters variations have different impacts on the behavioral strategy choices of stakeholders. From the perspective of government supervision, appropriately increasing rewards and penalties will help to promote the adoption of low-carbon construction programs by the power grid companies. However, the stronger rewards and penalties are not always better, and they can easily impose a financial burden on the government. From the construction perspective of the power grid companies, the behavioral strategy choices of the power grid companies are strongly influenced by the additional costs of low-carbon sustainable programs. The power grid companies need to consider the introduction of relevant technologies and equipment based on long-term benefits and appropriately increase their investments. From the perspective of public participation, the influence of public opinion has become a critical factor that cannot be ignored. The public positively or negatively impacts other stakeholders by commenting on the development programs of the government and the power grid companies. Similarly, low-carbon measures by the power grid companies and government will safeguard public benefits and promote positive public participation.

Finally, based on stakeholders’ behavioral strategy choices and different stages of the project life cycle, this study constructs a three-dimensional framework of the sustainable development mechanism for PCPs, which explains the complex relationships within PCPs and helps us to deeply understand the changes in the decision making of stakeholders. Combined with the analysis results, this study proposes strategies to promote the sustainable development of PCPs by constructing a dynamic reward and punishment mechanism, promoting the upgrading of low-carbon technologies, and encouraging the positive participation of the public.

With a new perspective on the life cycle of PCPs, this study creatively establishes a tripartite evolutionary game model comprising the government, power grid companies and public and explores the changes in the behavioral strategy choices of stakeholders in the long-term development of PCPs under the government-led mechanism, the collaborative participation mechanism, and the market-guided mechanism. Nevertheless, there are some limitations to this study. In this study, only the main factors influencing stakeholders’ decision-making are considered. As society progresses and technology develops, the relevant influencing factors as well as critical stakeholders may also change, which is exactly the issue that future studies need to focus on.