Reducing Carbon Emissions from Coal-Fired Power Plants: An Analysis Using Evolutionary Game Theory

Abstract

The promotion of energy conservation and emission reduction involves a multi-party game among governments, enterprises, and other stakeholders. To explore the game relationships among governments, the public, and coal-fired power enterprises under the “dual carbon targets”, this paper constructs an evolutionary game model for energy conservation and emission reduction involving three parties: the government, coal-fired power enterprises, and the public. Through a theoretical analysis and simulation analysis of the case study involving a central Hebei energy enterprise in China, the impact of parameter variations on the strategic choices of all parties and the evolutionarily stable strategies of the system is thoroughly discussed. The research findings indicate that reducing public supervision costs, increasing government rewards, subsidies, and penalties, and enhancing government regulatory capabilities are crucial factors in promoting energy-saving and emission-reduction efforts by coal-fired power enterprises. After multiple evolutionary iterations, the tripartite evolutionary game system ultimately reaches an evolutionarily stable state of government regulation, public supervision, and energy-saving and emission-reduction by coal-fired power enterprises at the point $E_8(\mathrm{1,1},1)$. Based on these findings, we propose a series of policy recommendations aimed at providing theoretical support for the Chinese government to achieve its energy-saving and emission-reduction strategies under the dual-carbon targets. These recommendations also offer practical guidance for the government in formulating emission reduction policies, for enterprises in optimizing their operational strategies, and for the public in participating in emission reduction efforts.

1. Introduction

Amidst the dire context of global climate change, achieving carbon peaking and neutrality (hereinafter referred to as “dual carbon” targets) has emerged as a global consensus and action agenda. As the world’s largest developing country and a responsible major power, China has unequivocally committed to reaching carbon peaking by 2030 and achieving carbon neutrality by 2060 [1,2,3]. This ambitious goal not only embodies China’s unwavering pledge to global climate governance, but also imposes stricter energy conservation and emission reduction requirements on various industries, including coal-fired power enterprises. Given their pivotal role in the energy supply and as a primary source of carbon emissions, the effectiveness of coal-fired power enterprises’ efforts in this regard is directly linked to the progress of China’s dual carbon targets [4,5,6,7].

According to official surveys, the proportion of coal-fired power generation in China is 63% [8]. Therefore, coal-fired power enterprises occupy a prominent position in China’s energy mix, yet their high carbon emissions make them a focal area for energy conservation and emission reduction. With the acceleration of energy transition, these enterprises confront the dual challenge of ensuring a secure energy supply while mitigating carbon emissions. Consequently, a thorough examination of their energy-saving and emission-reduction strategies under the dual carbon targets, alongside their influencing factors, is vital for advancing energy structure optimization and fostering green and low-carbon development [9,10]. Current research on energy conservation and emission reduction spans multiple domains, such as policy formulation, technological innovation, and market mechanisms. However, studies within the coal-fired power industry still exhibit gaps. On the one hand, existing research tends to concentrate on the binary game between governments and enterprises, overlooking the pivotal role of the public (including consumers, investors, etc.) in the process [11,12]. On the other hand, there is a lack of in-depth exploration into the intricate interaction mechanism among coal-fired power enterprises, governments, and the public [13].

As crucial participants and beneficiaries of energy conservation and emission reduction, the public plays an indispensable role in driving these efforts [14,15]. Their environmental monitoring awareness, consumption choices, and behavioral habits significantly impact the strategies adopted by coal-fired power enterprises. With the proliferation and enhancement of environmental awareness, an increasing number of individuals are paying attention to the carbon emissions of coal-fired power enterprises, exercising their oversight and advocacy powers, promoting the improvement of emission reduction policies, and favoring low-carbon, eco-friendly products and services [16]. This trend not only urges coal-fired power enterprises to strengthen their emission reduction efforts, but also prompts governments to enact stricter environmental policies and regulations.

In light of this, this paper aims to establish an evolutionary game model for energy conservation and emission reduction involving the government, coal-fired power enterprises, and the public under the dual carbon targets, grounded in evolutionary game theory. Through model construction and numerical simulation, we analyze the behavioral choices and dynamic evolution processes of each participant under different strategy combinations, explore the key factors influencing the effectiveness of coal-fired power enterprises’ emission reduction efforts, and propose corresponding policy recommendations. This research not only enriches the theoretical framework of energy conservation and emission reduction in the coal-fired power industry, but also provides practical guidance for governments in formulating reduction policies, enterprises in optimizing operational strategies, and the public in participating in emission reduction efforts.

2. Literature Review

This paper focuses on the following five aspects: Section 2.1 describes the current status and challenges of energy conservation and emission reduction in the coal-fired power industry; Section 2.2 shows the game studies between coal-fired power enterprises and governments; Section 2.3 explains the role of the public in energy conservation and emission reduction; Section 2.4 describes the deficiencies and extensions in tripartite evolutionary game research; and Section 2.5 states the application of evolutionary game theory in energy conservation and emission reduction.

2.1. Current Status and Challenges of Energy Conservation and Emission Reduction in the Coal-Fired Power Industry

In recent years, the escalating global concern over climate change has increasingly highlighted energy conservation and emission reduction in the coal-fired power generation industry as a focal point of research [17,18,19,20]. Coal-fired power generation, as a high-carbon emission segment of energy production, accounts for a significant proportion of the total global energy-related carbon emissions. According to statistical data from authoritative organizations such as the International Energy Agency, despite the rapid development of renewable energy posing a considerable impact on the coal-fired power generation industry, coal-fired power generation still maintains a pivotal position in the overall structure of global energy production, with its carbon emissions remaining substantial [21,22]. Therefore, effectively reducing carbon emissions from the coal-fired power generation industry while ensuring the security and stability of the global energy supply is not only a major test for this industry, but also a significant challenge faced collectively by the entire field of energy production and coal consumption.

2.2. Game Studies Between Coal-Fired Power Enterprises and Governments

Current research on energy conservation and emission reduction in the coal-fired power industry predominantly centers on the game relationship between enterprises and governments [23,24,25,26,27,28]. These studies, mostly based on game theory or evolutionary game theory, analyze the response strategies of coal-fired power enterprises to government measures such as carbon taxes, carbon emissions trading, and subsidy policies, and their impacts on the economy and environment. For instance, some studies indicate that government carbon emission restriction policies can incentivize coal-fired power enterprises to adopt more efficient power generation technologies and optimize energy structures for emission reduction [29]. Nevertheless, these studies often overlook the role of the public in the emission reduction process, leading to incomplete analytical frameworks.

2.3. The Role of the Public in Energy Conservation and Emission Reduction

As significant participants and promoters of energy conservation and emission reduction, the public’s environmental awareness, consumption choices, and behavioral habits significantly influence the strategies of coal-fired power enterprises. With the popularization of environmental education and the enhancement of public environmental awareness, more consumers are paying attention to the carbon emissions of coal-fired power enterprises, exercising oversight and advocacy, promoting the improvement of emission reduction policies, and favoring low-carbon, eco-friendly products and services [30,31,32]. This trend not only urges coal-fired power enterprises to strengthen their emission reduction efforts to meet market demands, but also prompts governments to enact stricter environmental policies and regulations to guide public behavior [33,34,35]. Therefore, incorporating the public into the game analysis framework of energy conservation and emission reduction in the coal-fired power industry is crucial for comprehensively understanding the emission reduction mechanism and formulating effective policies.

2.4. Deficiencies and Extensions in Tripartite Evolutionary Game Research

Although some scholars have attempted to incorporate multiple stakeholders into the game analysis of energy conservation and emission reduction, tripartite evolutionary game research (involving coal-fired power enterprises, governments, and the public) in the coal-fired power industry remains relatively scarce [36,37,38]. Most existing studies are limited to the dyadic game between coal-fired power enterprises and governments or involve multiple parties without deeply exploring the role of the public as a third party [39,40]. This research status restricts our comprehensive understanding of energy conservation and emission reduction in the coal-fired power industry. Consequently, this paper, building upon existing research, introduces the public as the third party in the game, establishing a tripartite evolutionary game model among coal-fired power enterprises, governments, and the public, aiming to fill this research gap. Through this model, we can delve deeper into the strategic choices and interaction mechanisms of each participant, revealing the key factors influencing the effectiveness of coal-fired power enterprises’ emission reduction efforts.

2.5. The Application of Evolutionary Game Theory in Energy Conservation and Emission Reduction

Evolutionary game theory provides a powerful tool for analyzing strategic choices and dynamic changes among different agents in complex systems. In the field of energy conservation and emission reduction, evolutionary game theory is widely applied to study the strategic interactions and evolutionary processes among governments, enterprises, and consumers [41,42,43,44]. By constructing evolutionary game models, it can reveal the impact of different strategic choices on the overall evolution of the system, providing a theoretical basis for formulating effective emission reduction policies [45,46,47]. In the research on energy conservation and emission reduction in the coal-fired power industry, introducing evolutionary game theory can more accurately simulate the strategic choices and dynamic changes among coal-fired power enterprises, governments, and the public, providing a more scientific basis for policy formulation.

In summary, grounded in existing research and considering the actual needs of energy conservation and emission reduction in the coal-fired power industry, this paper introduces the public as the third party in the game, constructing a tripartite evolutionary game model among governments, the public, and coal-fired power enterprises. Through numerical simulation and analysis, we explore the evolutionary paths and strategic choices of coal-fired power enterprises’ emission reduction efforts under the dual carbon targets, offering scientific guidance for governments in formulating emission reduction policies, enterprises in optimizing operational strategies, and the public in participating in emission reduction efforts.

3. Model Construction

3.1. Problem Description

The dynamic mechanism system, which encompasses three key entities, the government, the public, and coal-fired power enterprises, is illustrated in Figure 1. Firstly, within this mechanism, the government plays the role of policymaker and regulator. By implementing environmental taxes, enforcing environmental penalties, providing financial subsidies, and conducting necessary supervision, the government aims to guide and constrain the energy-saving and emission-reduction behaviors of coal-fired power enterprises. The fundamental objective of the government is to achieve the dual goals of environmental protection and economic development, thereby motivating coal-fired power enterprises to actively engage in energy-saving and emission-reduction efforts.

Secondly, coal-fired power enterprises serve as direct participants in energy-saving and emission-reduction initiatives. While pursuing economic benefits, these enterprises also face significant pressure from environmental protection. Their behavioral choices are driven not only by their own business strategies, but also by government policies and market demands. Therefore, coal-fired power enterprises need to find a balance between economic benefits and environmental protection and decide whether to adopt energy-saving and emission-reduction strategies.

Lastly, the public plays a dual role in environmental protection as both participants and supervisors. They influence the energy-saving and emission-reduction behaviors of coal-fired power enterprises through their decision to supervise or not. The behavioral choices of the public are often driven by both environmental awareness and personal interests. With the continuous enhancement of environmental awareness, the public has become increasingly concerned about the energy-saving and emission-reduction efforts of coal-fired power enterprises and is willing to actively participate and play a supervisory role.

3.2. Model Assumptions

In the tripartite evolutionary game of energy conservation and emission reduction, the government, the public, and coal-fired power enterprises constitute the three core stakeholders. Each of these stakeholders aims to maximize their own interests. During the game, information is not fully symmetric, and all three stakeholders are boundedly rational, adjusting their strategies by anticipating those of the other two parties, ultimately forming a set of behavioral strategies for all three. Based on this, the following assumptions are proposed.

Assumption 1. 

The government considers energy conservation and emission reduction, with its strategy set as {regulation, non-regulation} and its corresponding probability set as {$x, 1-x\}$. The public also considers energy conservation and emission reduction, with its strategy set as {supervision, non-supervision} and its corresponding probability set as {$y, 1-y$}. Coal-fired power enterprises primarily weigh whether energy conservation and emission reduction can bring benefits to themselves, with their strategy set as {conservation and reduction, non-conservation and non-reduction} and their corresponding probability set as {$z, 1-z$}.

Assumption 2. 

When the government chooses to regulate, it incurs a regulatory cost $A_1$. To incentivize public supervision, the government offers a whistleblower reward D. To encourage coal-fired power enterprises to adopt conservation and reduction measures, the government provides subsidies E. If coal-fired power enterprises cause environmental pollution and are caught, the government imposes a fine H, increasing their environmental violation costs. Government regulation helps reduce environmental pollution incidents, generating an environmental benefit denoted as $P_1$.

Assumption 3. 

if coal-fired power generation enterprises do not implement energy-saving and emission-reduction measures, the government may incur losses due to increased environmental governance costs and damage to their reputation and image, denoted as $K_1$.

Assumption 4. 

When the public chooses to supervise, they use methods such as reporting and petitioning to express environmental concerns, incurring a corresponding cost $A_2$. Through public supervision, the government is prompted to address environmental issues, generating an environmental benefit $P_2$. If the government adopts a regulatory strategy, it will oversee the rectification of coal-fired power enterprises, who will then pay negative externality compensation and environmental restoration costs W to the public. If the public chooses not to supervise, they must endure the negative externalities of the environment.

Assumption 5. 

When coal-fired power enterprises choose to conserve and reduce, they incur costs $A_4$ related to environmental governance and the research and development of conservation and reduction technologies. Implementing conservation and reduction measures enhances capacity utilization, bringing benefits $R_1$to the enterprises. It also avoids environmental penalties H and reduces the tax burden associated with conservation and reduction taxes, where the post-conservation and reduction environmental tax is denoted as $F_1$. Furthermore, it can mitigate the risks of conservation and reduction by absorbing government subsidies E. After conservation and reduction measures are implemented, the environment improves, generating additional environmental benefits ∆P.

Assumption 6. 

when coal-fired power enterprises choose not to conserve and reduce, they obtain a revenue $R_2$ but may face environmental penalties H, higher environmental taxes $F_2$, environmental damage ∆K, and reputational and image losses $K_2$.

Based on realistic conditions and model assumptions, a payment matrix for the energy-saving and emission-reduction mechanism involving governments, the public, and coal-fired power enterprises can be constructed, as shown in

Table 1. Evolutionary Game Payoff Matrix.

	Coal-Fired Power Enterprise		Government
			$\mathbf{Regulation}\mathit{x}$	$\mathbf{Non-Regulation} 1-\mathit{x}$
	supervised $y$	energy saving and emission reduction$z$	${-A}_1-E-D+F_1+∆P+P_1,$ $-A_2+D+P_2+∆P,$ $-A_4+E+R_1-F_1$	$F_1-K_1+∆P,$ $-A_2+P_2+∆P,$ $-A_4+R_1-F_1$
The public		No energy saving or emission reduction $1-z$	$-A_1-D+F_2+H+P_1-∆K,-A_2+D+M+P_2-∆K,$ $R_2-F_2-H-M-K_2$	$F_2+H-K_1-∆K,$ $M-A_2+P_2-∆K,$ $R_2-F_2-H-M-K_2$
	non-supervised $1-y$	energy saving and emission reduction$z$	${-A}_1-E+F_1+∆P+P_1,$ $∆P,$ $-A_4+E+R_1-F_1$	$F_1-K_1+∆P,$ $∆P,$ $-A_4+R_1-F_1$
		no energy saving or emission reduction $1-z$	$-A_1+F_2+H+P_1-∆K,$ $-∆K,$ $R_2-F_2-H-K_2$	$F_2+H-K_1-∆K,$ $-∆K,$ $R_2-F_2-H-K_2$

.

3.3. Construction of Replication Dynamic Equations

Based on Table 1, the expected payoff for the government’s regulatory strategy ($E_{11}$), the expected payoff for the non-regulatory strategy ($E_{12}$), and the replication dynamic equation G(x) can be derived as follows:

$$\begin{gathered} E_{11}=zy\left(-A_1-E-D+F_1+∆P+P_1\right)+z\left(1-y\right)\left(-A_1-E+F_1+∆P+P_1\right) \\ +y\left(1-z\right)\left(-A_1-D+F_2+H+P_1-∆K\right)+(1-z)(1-y)(-A_1+F_2+H \\ +P_1-∆K) \end{gathered}$$

$$\begin{gathered} E_{12}=zy\left(F_1-K_1+∆P\right)+z\left(1-y\right)\left(F_1-K_1+∆P\right)+y\left(1-z\right)\left(F_2+H-K_1-∆K\right) \\ +(1-z)(1-y)(F_2+H+K_1-∆K) \end{gathered}$$

$$G\left(x\right)=x\left(1-x\right)\left(E_{11}-E_{12}\right)=x(1-x)(-zE-A_1+P_1-Dy+K_1-z{K}_1)$$

The expected payoff for the public’s supervision strategy ($E_{21}$), the expected payoff for the non-supervision strategy ($E_{22}$), and the replication dynamic equation G(y) are:

$$\begin{gathered} { E}_{21}=zx\left(-A_2+D+P_2+∆P\right)+z\left(1-x\right)\left(-A_2+P_2+∆P\right) \\ +x\left(1-z\right)\left(-A_2+D+M+P_2-∆K\right)+(1-x)(1-z)(-A_2+M+P_2-∆K) \end{gathered}$$

$$E_{22}=xz∆p+z∆p\left(1-x\right)-x∆k\left(1-z\right)-∆k\left(1-x\right)\left(1-z\right)$$

$$G\left(y\right)=y\left(1-y\right)\left(E_{21}-E_{22}\right)=y(1-y)(Dx-A_2+M+P_2-zM)$$

The expected payoff for coal-fired power enterprises’ energy-saving and emission-reduction strategies ($E_{31}$), the expected payoff for not adopting such strategies ($E_{32}$), and the replication dynamic equation G(z) are:

$$\begin{gathered} { E}_{21}=zx\left(-A_2+D+P_2+∆P\right)+z\left(1-x\right)\left(-A_2+P_2+∆P\right) \\ +x\left(1-z\right)\left(-A_2+D+M+P_2-∆K\right)+(1-x)(1-z)(-A_2+M+P_2-∆K) \end{gathered}$$

$$E_{22}=xz∆p+z∆p\left(1-x\right)-x∆k\left(1-z\right)-∆k\left(1-x\right)\left(1-z\right)$$

$$G\left(y\right)=y\left(1-y\right)\left(E_{21}-E_{22}\right)=y(1-y)(Dx-A_2+M+P_2-zM)$$

3.4. Analysis of System Equilibrium Points and Stability

By setting $G\left(x\right)=0, G\left(y\right)=0,$ and $G\left(z\right)=0$ in the dynamic system equations for the government, the public, and coal-fired power enterprises, eight pure strategy equilibrium points are identified:$E_1 (\mathrm{0,0},0), E_2 (\mathrm{1,0},0),$ $E_3\left(\mathrm{0,1},0\right), E_4 \left(\mathrm{0,0},1\right),$ $E_5 \left(\mathrm{1,1},0\right), E_6 \left(\mathrm{1,0},1\right), E_7 (\mathrm{0,1},1),$ and $E_8(\mathrm{1,1},1).$ The evolutionary stability of these equilibrium points is determined by the signs of the eigenvalues of the Jacobian matrix. An equilibrium point is considered evolutionarily stable if all eigenvalues of its Jacobian matrix are non-positive; otherwise, it is unstable.

Let $a={-A}_1+P_1,b=-A_4+E+R_1-F_1,c=F_1-F_2-H-K_2,d=R_2-F_2-H-M-K_2,$ based on the aforementioned replication dynamic system, and the Jacobian matrix is formulated as:

$$\mathrm{J}=\left[\begin{array}{ccc}{\displaystyle \frac{dG\left(x\right)}{dx}}& {\displaystyle \frac{dG\left(x\right)}{dy}}& {\displaystyle \frac{dG\left(x\right)}{dz}}\\ {\displaystyle \frac{dG\left(y\right)}{dx}}& {\displaystyle \frac{dG\left(y\right)}{dy}}& {\displaystyle \frac{dG\left(y\right)}{dz}}\\ {\displaystyle \frac{dG\left(z\right)}{dx}}& {\displaystyle \frac{dG\left(z\right)}{dy}}& {\displaystyle \frac{dG\left(z\right)}{dz}}\end{array}\right]$$

$$=\left[\begin{array}{ccc}{C}_{11}& D\mathrm{x}(\mathrm{x}-1)& \mathrm{x}(\mathrm{x}-1)(E+K_1)\\ D\mathrm{y}(1-\mathrm{y})& C_{22}& M\mathrm{y}(1-\mathrm{y})\\ \mathrm{z}(1-\mathrm{z})E& \mathrm{z}(1-\mathrm{z})M& C_{33}\end{array}\right]$$

$$\left\{\begin{array}{l}{C}_{11}=(1-2x)(-zE-A_1+P_1-Dy+K_1-z{K}_1)\\ C_{22}=\left(1-2y\right)\left(Dx-A_2+M+P_2-zM\right)\\ C_{33}=\left(1-2z\right)\left(xE-A_4+R_1-F_1+My-R_2+F_2+H+K_2\right)\end{array}\right.$$

Each of the eight pure strategy equilibrium points is substituted into the Jacobian matrix, and the specific eigenvalues and their stability scenarios are derived under the basic conditions set forth in the assumptions, as presented in

Table 2. Local stability analysis of equilibrium points.

Equilibrium Points	Eigenvalue 1	Eigenvalue 2	Eigenvalue 3	Eigenvalue Symbol	Stability
$(\mathrm{0,0},0)$	$a+K_1$	$b$	${-A}_4+R_1-R_2-c$	($+,X,-$)	unstable
$(\mathrm{1,0},0)$	$-a-K_1$	$b-d$	$E{-A}_4+R_1+R_2-c$	($-,+,X$)	unstable
$(\mathrm{0,1},0)$	$a-D+K_1$	$-b$	$-A_4+R_1+M-c$	($X, X, X$)	ESS
$(\mathrm{0,0},1)$	$a-E$	$b$	$A_4-R_1+R_2-c$	(+$, X, X$)	unstable
$(\mathrm{1,1},0)$	$D-a-K_1$	$-b+d$	$E-A_4+M+R_1-c$	($X,-,+$)	unstable
$(\mathrm{1,0},1)$	$E-a$	$b-d$	$-E+A_4-R_1+R_2+c$	($-,+, X$)	unstable
$(\mathrm{0,1},1)$	$a-E-D$	$-b$	$A_4-R_1-M+c$	(+$, X, X$)	unstable
$(\mathrm{1,1},1)$	$E+D-a$	$-b+d$	${-E+A}_4-R_1-M+c$	($X, X, X$)	ESS

.

Given that all parameters related to the government, the public, and coal-fired power enterprises in the model are positive, equilibrium points $E_1(\mathrm{0,0},0), E_2(\mathrm{1,0},0),{ E}_4(\mathrm{0,0},1),$ ${ E}_5 (\mathrm{1,1},0),E_6 (\mathrm{1,0},1)$, and $E_7(\mathrm{0,1},1)$ contain non-negative eigenvalues, violating Lyapunov’s first method of stability analysis, thereby confirming their instability. Furthermore, under the current national context of vigorously advocating energy saving and emission reduction, it is impractical for both the government and the public to ignore the environmental pollution caused by the extensive development of coal-fired power enterprises. Consequently, equilibrium point $E_1(\mathrm{0,0},0)$ is not considered.

Scenario 1: When the inequalities $a-D+K_1<0,$ $b>0,$ and $-A_4+R_1+M-c<0$ hold, point $E_3\left(\mathrm{0,1},0\right)$ represents an evolutionary stable strategy. However, it is an undesirable stable point because it fails to achieve the goal of promoting energy conservation and emission reduction in coal-fired power enterprises.

Scenario 2: When the inequalities $E+D-a<0,$ $-b+d<0,$ and ${-E+A}_4-R_1-M+c<0$ hold, point $E_8(\mathrm{1,1},1)$ represents an evolutionarily stable strategy. It is a desirable stable point because it achieves the goal of promoting energy conservation and emission reduction in coal-fired power enterprises. Furthermore, strict government regulations can reduce the risks associated with energy conservation and emission reduction in these enterprises and encourage public oversight.

4. Numerical Simulation

4.1. Case Selection and Parameters Allocation

In the context of the dual carbon targets, coal-fired power enterprises, as a crucial component of the energy industry, play a vital role in the transformation path towards energy conservation and emission reduction for achieving the country’s overall carbon reduction objectives. This paper selects a large coal-fired power enterprise as the research case. Founded in 2008, Jizhong Energy Group Co., Ltd. boasts an industrial presence across 14 provinces and regions, including Hebei, Shanxi, Shaanxi, Inner Mongolia, Xinjiang, and others. The company possesses abundant coal resources and sophisticated coal-fired power generation technologies. However, with the increasingly stringent national restrictions on carbon emissions, Coal-Fired Power Enterprise A faces significant pressure to conserve energy and reduce emissions.

Over the past few years, Jizhong Energy has actively taken measures such as introducing advanced coal-fired power generation technology, constructing carbon capture and storage (CCS) facilities, and improving the energy utilization efficiency to address the challenges posed by the dual carbon targets. Additionally, the enterprise has engaged in extensive cooperation with stakeholders, including the government and the public, to jointly promote the development of energy conservation and emission reduction.

The specific reasons for selecting Jizhong Energy as the case study are as follows: (1) Jizhong Energy is highly representative in the coal-fired power industry, and its energy conservation and emission reduction measures and transformation path provide important references for other coal-fired power enterprises. (2) Jizhong Energy maintains close cooperation with stakeholders, including the government and the public, which can better reflect the actual situation of multi-party games under the dual carbon targets. (3) Jizhong Energy possesses abundant data and experience in energy conservation and emission reduction, providing reliable data support for the numerical simulations conducted in this paper.

In the implementation of energy conservation and emission reduction, the collaborative efforts among Jizhong Energy, the public, and the government primarily focus on optimizing the efficiency and quality of these initiatives. This collaborative endeavor aims to propel the rapid development of energy conservation and emission reduction within Jizhong Energy, accelerate industrial upgrading, and ultimately elevate the national strategy for energy conservation and emission reduction. Furthermore, the strategic choices of these three parties serve as the core among numerous complex factors influencing energy conservation and emission reduction, and subtle changes in these parties and variables may alter the evolutionary trajectory of the government’s energy conservation and emission reduction efforts, leading to diversified stable strategies.

Building upon existing evolutionary game models, this study further employs numerical simulation methods to delve into the specific paths of a strategic evolution among Jizhong Energy, the public, and the government in complex dynamic environments. During the simulation process, parameter settings closely align with the dynamic fluctuations of various factors in the model and their high sensitivity to the system’s stable strategies. We systematically adjusted the core parameters including costs, rewards and penalties, and benefits, and conducted a detailed analysis of how these factors subtly influence the strategic choices of each participant.

It should be clarified that the parameter values set in this paper are solely for theoretical analysis, such as $A_1=15,D=8,E=10,H=10,P_1=35,K_1=20,A_2=22,P_2=20,M=10$, $A_4=60,R_1=45,F_1=6,R_2=35,F_2=12,K_2=16;$ this setup enables the research to focus precisely on the internal mechanisms and dynamic changes of evolutionarily stable strategies in the process of energy conservation and emission reduction, providing profound and insightful guidance for policymakers.

4.2. Simulation Analysis of Evolutionarily Stable Strategies for Jizhong Energy, the Public, and the Government

Based on the simulated parameter configurations, we can clearly observe the strategic evolution trajectories of Jizhong Energy, the public, and the government under specific conditions. Under the premise of satisfying all assumed conditions, we initiated the game with x, y, and z set to 0.2, 0.5, and 0.8, respectively, while keeping other parameters constant, resulting in the outcomes depicted in Figure 2.

As shown in Figure 3, with the increasing probabilities of the government choosing to regulate Jizhong Energy (x) and the public choosing to supervise coal-fired power enterprises (y), both the government and the public exhibit a trend of accelerated convergence towards participation, shortening the evolutionary time frame. For the government, as x and y rise, its action rate decreases, which is attributed to the active evolution of participation by both parties, leading to a gradual weakening of the government’s role and a corresponding reduction in support intensity to save fiscal expenditures. Additionally, the chart also indicates that as z increases, the willingness of both the government and the public to participate strengthens, and coal-fired power enterprises also intensify their efforts in energy conservation and emission reduction as their willingness to do so improves.

Furthermore, it is noteworthy that even starting from such a low initial point, the system undergoes self-adjustment and continuous evolution, ultimately converging to a stable point $(\mathrm{1,1},1)$ when key factors such as benefits, profit distribution ratios, and costs remain within appropriate ranges. This emphasizes that as time passes and strategies align, Jizhong Energy, the public, and the government continuously adjust their strategies, ultimately forming a stable and efficient “energy conservation and emission reduction-supervision-regulation” model. This finding not only validates the rationality and effectiveness of the theoretical model, but also provides a solid theoretical foundation for practical decision making, emphasizing the feasibility of guiding and promoting long-term stable strategies for all parties involved in the process of energy conservation and emission reduction through the scientific regulation of relevant factors.

4.3. Simulation Analysis of Tripartite Evolutionary Stability in the Process of Energy Conservation and Emission Reduction

Under the conditions of $E+D-a<0,-b+d<0,$ and $-E+A_4-R_1-M+C<0,$ the initial parameters were set to $x=0.5,y=0.5,z=0.5,A_1=15,D=8,E=10,H=10,P_1=35,K_1=20,A_2=22,P_2=20,M=10,A_4=60,R_1=45,F_1=6,R_2=35,F_2=12,K_2=16$, and $(0.5,0.5,0.5)$ was used as the initial strategic combination representing the willingness of Jizhong Energy, the public, and the government. Fifty simulations were conducted for the tripartite evolution in the process of energy conservation and emission reduction, with the results shown in Figure 3. It is evident from Figure 3 that the tripartite evolutionary equilibrium point in the process of energy conservation and emission reduction is $E_8(\mathrm{1,1},1)$, i.e., (government regulation, public supervision, Jizhong Energy’ energy conservation and emission reduction).

Under the conditions of $a-D+K_1<0,b>0,$ and $-A_4+R_1+M-C<0,$ the initial parameters were set to ${x=0.5,y=0.5,z=0.5,A}_1=15,D=8,$ $E=10,H=10,P_1=35,$ $K_1=20,A_2=22,P_2=20,M=10,A_4=60,R_1=45,F_1=6,R_2=35,F_2=12,K_2=16.$ Using $(0.5, 0.5, 0.5)$ as the initial strategic combination representing the willingness of the three parties, fifty simulations were conducted for the tripartite evolution in the process of energy conservation and emission reduction, with the results shown in Figure 4. As shown in Figure 4, the tripartite equilibrium point in the process of energy conservation and emission reduction is $E_3(\mathrm{0,1},0)$, i.e., (no government regulation, public supervision, no energy conservation, and emission reduction by Jizhong Energy).

4.4. Sensitivity Analysis of Public Supervision Cost ($A_2$) on Public Strategic Choice

In this study, five simulation runs were conducted by adjusting different values of the public supervision cost ($A_2=22,24,26,28,30$), while keeping other parameters constant. The results are shown in Figure 5.

A more comprehensive analysis of the five simulation results emphasizes the significant impact of the $A_2$ value on the convergence speed of public strategic choices. Specifically, as $A_2$ decreases, the convergence speed towards 1 (representing a state of strict monitoring) accelerates significantly, with the shortest time required. This indicates that when monitoring costs are low, the public tends to strictly monitor the energy-saving and emission-reduction behaviors of Jizhong Energy, as the expected benefits from such strict monitoring may exceed the costs associated with non-monitoring. Conversely, as $A_2$ increases, the convergence speed towards 1 gradually weakens, and the system shifts towards convergence at 0, suggesting an increased likelihood of the public choosing a non-monitoring strategy.

4.5. Sensitivity Analysis of Variations in Rewards (E) and Penalties (H) on the Strategic Choices of Jizhong Energy

With other parameter values held constant, this study conducted simulation analyses by setting multiple gradient levels for rewards (E) provided to Jizhong Energy when choosing energy saving and emission reduction, and penalties (H) imposed when choosing not to do so. Specifically, the variations in rewards (E) were set at 7, 8, 9, 10, and 11, while penalties (H) were adjusted to 7, 8, 9, 10, and 11. Through five iterations of simulations, we delved into the dynamic changes in the strategic choices of Jizhong Energy as E and H varied, with the results presented in Figure 6 and Figure 7.

Figure 6 visually demonstrates the impact of government-provided regulatory rewards (E) on the strategic choices of Jizhong Energy. When the rewards for energy saving and emission reduction (E) provided by the government are low (e.g., E = 7), the probability of Jizhong Energy choosing energy saving and emission reduction significantly decreases, approaching the choice of not doing so, reflecting inadequate government incentives to stimulate their willingness to engage in energy saving and emission reduction. As the E value gradually increases, so does the probability of Jizhong Energy choosing energy saving and emission reduction. Once E exceeds 9, the trend leans towards comprehensive energy saving and emission reduction (i.e., a probability of 1), and the higher the E value, the faster the convergence speed. This robustly validates the effectiveness of government incentives in promoting energy saving and emission reduction among Jizhong Energy.

On the other hand, Figure 7 reveals the significant impact of penalties (H) on the behavioral choices of Jizhong Energy. When penalties (H) are low (e.g., H = 7), the costs for coal-fired power enterprises not engaging in energy-saving and emission-reduction practices are correspondingly low, leading to a reduced probability of engaging in such activities and a tendency to opt out. However, as the H value increases, especially reaching higher levels (e.g., H = 9), the probability of Jizhong Energy engaging in energy-saving and emission-reduction activities rapidly rises, tending towards higher levels of energy-saving and emission-reduction practices (with a probability of 1 in the context of potential standardization or proportional representation considered in the model). This suggests that severe penalties for non-compliance can effectively constrain corporate behavior and, driven by the pursuit of profit maximization, motivate enterprises to fulfill energy-saving and emission-reduction agreements and actively participate in them.

A further comparison of the simulation results for rewards (E) and penalties (H) reveals that an increase in either E or H to 9 is sufficient to guide both the public and coal-fired power enterprises towards joint participation in energy saving and emission reduction. This finding emphasizes the rapid effectiveness of government incentives and penalties in promoting the willingness of coal-fired power enterprises to engage in energy-saving and emission-reduction practices and fostering joint participation by both the public and these enterprises. Additionally, it indicates that compared to penalties (H), rewards (E) have equal incentive power and efficiency in triggering joint participation in energy-saving and emission-reduction activities between the public and Jizhong Energy. Therefore, when formulating relevant policies, the government should weigh the synergistic effects of rewards and penalties, adopting both incentive measures and penalties in a coordinated manner to establish a more effective incentive mechanism.

4.6. Sensitivity Analysis of Variations in Government Regulation Costs ($A_1$) on Government Strategic Choices

Based on the aforementioned figures and tables, in the scenario of escalating government regulation costs ($A_1$), as these costs increase, governments tend to adopt regulatory strategies at a gradually decreasing pace, accompanied by a slight increase in the duration of evolution, as illustrated in Figure 8. This is attributed to the fact that as government regulation costs rise, fiscal expenditures also increase, thereby intensifying the financial pressure on governments. Consequently, the pace of adopting regulatory strategies slows down. This robustly validates the effectiveness of government regulation in promoting energy conservation and emission reduction among Jizhong Energy, while also indicating that as government regulation costs increase, the willingness of governments to regulate gradually decreases.

5. Discussion

The research findings of this paper indicate that under the dual carbon targets, the evolutionary game of energy conservation and emission reduction among the government, coal-fired power enterprises, and the public is a complex and dynamic process. By constructing a tripartite evolutionary game model and conducting a numerical simulation analysis, we reveal the impact of different parameter changes on the strategic choices of all parties involved, as well as the stable strategies of system evolution.

Firstly, the public monitoring cost ($A_2$) has a significant impact on the strategic choices of the public. When the monitoring cost is low, the public is more inclined to choose the monitoring strategy, as the expected benefits of monitoring may exceed the cost at this time. However, as the monitoring cost increases, the likelihood of the public choosing the non-monitoring strategy also increases. This finding emphasizes the importance of reducing public monitoring costs to enhance public participation and promote energy conservation and emission reduction efforts.

Secondly, the rewards (E) and penalties (H) provided by the government have a crucial impact on the strategic choices of coal-fired power enterprises. When the rewards for energy conservation and emission reduction provided by the government are low, the willingness of coal-fired power enterprises to adopt such measures decreases significantly. As the rewards increase, the probability of coal-fired power enterprises choosing energy conservation and emission reduction also rises. Similarly, when the penalties for not adopting energy conservation and emission reduction measures are low, coal-fired power enterprises are more inclined to choose the non-energy conservation and emission reduction strategy. However, as the penalties increase, the probability of coal-fired power enterprises adopting energy conservation and emission reduction measures rises rapidly. This result validates the effectiveness of government incentives and penalties in promoting energy conservation and emission reduction among coal-fired power enterprises.

Furthermore, changes in government regulatory costs ($A_1$) also affect the government’s strategic choices. As regulatory costs increase, the government tends to adopt regulatory strategies at a gradually decreasing speed. This is mainly because the rise in regulatory costs exacerbates the government’s financial pressure, leading to a slowdown in the adoption of regulatory strategies. However, despite the gradual decrease in the government’s willingness to regulate, the effectiveness of government regulation in promoting energy conservation and emission reduction among coal-fired power enterprises remains validated.

When exploring the stable strategies of the tripartite evolutionary game, we find that when certain conditions are met, the system can converge to an ideal stable point $(\mathrm{1,1},1)$, namely, government regulation, public monitoring, and energy conservation and emission reduction by coal-fired power enterprises. The realization of this stable strategy requires the joint efforts and collaboration of the government, coal-fired power enterprises, and the public. The government needs to provide effective incentive measures and penalty mechanisms, coal-fired power enterprises need to actively fulfill their responsibilities for energy conservation and emission reduction, and the public needs to actively participate in monitoring.

However, we also note that there are some challenges and difficulties in practical operations. For example, the rise in government regulatory costs may limit the government’s regulatory capacity, coal-fired power enterprises may face dual pressures of technology upgrading and cost control for energy conservation and emission reduction, and there may be differences in the public’s awareness and ability to monitor. Therefore, when formulating and implementing energy conservation and emission reduction policies, it is necessary to fully consider the influence of these factors and take targeted measures to address them.

6. Conclusions, Suggestions, and Limitations

6.1. Conclusions

Based on evolutionary game theory, this paper constructs an evolutionary game model for energy conservation and emission reduction involving the government, coal-fired power enterprises, and the public. Through numerical simulation and empirical analysis, we reveal the impact of different parameter changes on the strategic choices of all parties involved and the stable strategies of system evolution. The research results indicate that reducing public monitoring costs, increasing government rewards and penalties, and strengthening the government’s regulatory capacity are key factors in promoting energy conservation and emission reduction among coal-fired power enterprises. Meanwhile, the collaborative cooperation among the government, coal-fired power enterprises, and the public is an important guarantee for achieving energy conservation and emission reduction targets. When the inequalities $E+D-a<0,$ $-b+d<0,$ and ${-E+A}_4-R_1-M+c<0$ hold, an evolutionary stable state is achieved at point $E_8(\mathrm{1,1},1)$. At this evolutionarily stable point E8 within the system, the government, coal-fired power enterprises, and the public work together to accomplish the goal of promoting energy conservation and emission reduction in coal-fired power generation.

6.2. Suggestions

The government should increase investment in energy conservation and emission reduction efforts, improve the regulatory capacity, and reduce regulatory costs. At the same time, more scientific and reasonable incentive measures and penalty mechanisms should be formulated to stimulate the willingness of coal-fired power enterprises to adopt energy conservation and emission reduction measures and enhance public participation.

Coal-fired power enterprises should actively fulfill their responsibilities for energy conservation and emission reduction, increase investment in technology research and development, and improve the feasibility and economy of energy conservation and emission reduction technologies. At the same time, they should strengthen communication and cooperation with the government and the public to jointly promote the in-depth development of energy conservation and emission reduction efforts.

The public should enhance their environmental awareness and actively engage in energy conservation and emission reduction efforts. They can voice their environmental concerns through reporting and appealing, thereby urging the government to address environmental issues and overseeing coal-fired power enterprises to intensify their energy conservation and emission reduction measures.

6.3. Limitations

This paper assumes that all parties are boundedly rational agents, but in practical operations, the decisions of all parties may be influenced by more complex factors, such as political, economic, and social factors. Therefore, these factors can be further considered in subsequent research to investigate their impact on the strategic choices of all parties involved.

The numerical simulation parameters set in this paper are based on a theoretical analysis and hypothetical values and do not directly correspond to specific values in the real economic and social environment. Therefore, in subsequent research, more accurate parameter values can be obtained through field research and data analysis to improve the accuracy and practicality of the model.

This paper mainly focuses on the issue of energy conservation and emission reduction in the coal-fired power industry, but energy conservation and emission reduction efforts involve multiple industries and fields. Therefore, subsequent research can further expand the research scope to explore the issues of energy conservation and emission reduction in other industries and fields and their influencing factors.