Evolutionary Game Analysis of Government Regulation on Green Innovation Behavior Decision-Making of Energy Enterprises

Abstract

Encouraging environmentally friendly innovation in energy companies is an essential way to stop global warming. Through ingenious integration of reputation and fairness preference, this research develops an evolutionary game model between the government and energy companies. This research investigates the dynamic evolution of green innovation strategy selection by energy firms operating under government supervision, using an evolutionary game model as a basis. This study examines how government regulations, including their subsidies and penalties, reputation, and fairness preference, affect the green innovation behavior of energy enterprises. The research shows that without considering the fairness preference, the subsidy and punishment of government regulation can improve the tendency of energy enterprises to choose green innovation behavior. At the same time, considering the reputation of energy enterprises to assume social responsibility can improve the tendency of energy enterprises to choose green innovation behavior. In the case of considering fairness preference, energy companies with strong fairness preference are more likely not to adopt green innovation and need more subsidies and penalties to choose green innovation; energy enterprises with weak fairness preference are more likely to adopt green innovation; green innovation will take place with fewer subsidies and penalties; reputation plays a stronger role in energy companies with weak fairness preferences. The study can give the government a theoretical foundation on which to build precise regulatory plans for various energy firms and encourage green innovation in those enterprises.

1. Introduction

Global warming has caused an ecological crisis that is currently a global problem that poses a severe threat to the continued growth of humankind [1,2]. As a result, nations are aggressively tackling climate change and investigating development models that reduce emissions and use less energy [3]. The ability of an organization to produce sustainably and function as a major force in economic development is closely correlated with its green innovation [4]. The government aims to gradually reduce carbon emissions by enhancing enterprises’ green innovation capabilities [5].

In the energy industry, green innovation is a gradual process. During this process, government policies and regulations play a crucial role. Influenced by the government and society, energy enterprises continuously adjust their behavior choices. The way that the government approaches green innovation through policy and regulation is crucial in both directing and constraining the choices that energy companies make. Balancing the interests of multiple stakeholders while maximizing green innovation in energy enterprises is a challenging issue for government decision-making. The research content of this paper is the research on the regulation strategy of the government to promote the green innovation of energy enterprises. The research structure of this paper is as follows: The first part is the introduction. The second part is a literature review. The third part is the construction and hypothesis of the model. The fourth part is the stability analysis of energy enterprise strategy. The fifth part is the analysis of the stability of government strategy. The sixth part is the equilibrium point and stability analysis of the evolutionary game system. The seventh part is the simulation analysis. The eighth part is the discussion. The ninth part is the conclusion.

2. Literature Review

The impact of government regulation on energy enterprises: government regulation primarily controls the carbon emissions, performance, and pollutant discharge behaviors of energy enterprises through regulations, market mechanisms, and technical standards. Environmental regulation and policy regulation are the two areas of research on how regulations affect energy firms. The government stipulates the emission behaviors of energy enterprises by establishing a legal system and restricts their environmental damage through supervision [6,7]. The other research, which is based on environmental regulation, looks at how enterprise innovation activities are affected by heterogeneous environmental regulation and supports sustainable development [8]. The government intervenes in business conduct through rules and regulations to accomplish energy conservation and emission reduction [9,10]. The government has adopted laws and regulations to reasonably allocate the environmental management rights of energy companies to influence their pollutant emissions [11]. The other study similarly investigates how government policies affect China’s new energy enterprises’ performance in terms of innovation [12]. An acceptable coordination mechanism between the government and energy firms is developed in the research of market mechanisms in order to form a reasonable market mechanism for carbon constraints [13,14]. The market mechanism formed by the distortion of the factor market plays a huge role in strengthening market supervision by the government and increasing the profit growth of energy enterprises [15]. According to research on technological control and subsidies, in order to achieve the low-carbon transformation of businesses, the government provides financial support for new energy firms’ innovative business models [16]. To encourage green technology innovation in energy companies and enhance their environmental performance, the government mandates energy-oriented technical advancement [17].

Studies on the effects of green innovation in the energy sector: Enterprise green innovation is primarily influenced by laws, policies, market dynamics, and future development trends. Through the implementation of pertinent laws, rules, and supportive policies, government policies and regulations play a crucial role in influencing the green innovation behaviors of enterprises. The specific ways include the introduction of green finance [18,19], green credit [20,21,22,23], green fiscal policy [24], green bonds [25], uncertain economic policy [26], energy conservation and emission reduction policy [27], environmental regulation [28,29], dual carbon policy [30], and corporate political participation [31]. The market environment primarily influences the green innovation of energy enterprises by affecting their strategies and initiatives. The main market changes include the opening of the carbon trading market [32], energy use right trading [33], and stock market liberalization [34]. Future development trends have a big impact on energy companies’ green innovation. The influence that energy enterprises exert over global future development trends affects their green innovation efforts, including digital transformation [35,36], digital economy [37,38], environmental management system certification [39], new urbanization [40], green mergers and acquisitions [41], and industrial robots [42].

Studies on green innovation’s evolutionary game in energy businesses: In addition to examining the strategic interactions between the government, businesses, and the public, this study applies game theory to the enterprise economy. It focuses on the strategic decisions made by the government and businesses. Research on government regulation: The other study uses evolutionary game analysis to investigate the ways in which three environmental regulating instruments, and different combinations of them, impact new energy businesses’ green technology innovation practices [43]. The other study uses evolutionary game theory to examine how environmental legislation affects green technology innovation activities among the government, private sector, polluting enterprises, and pollution-free companies [44]. By examining the tri-partite evolutionary game model of the influx and outflow governments and energy-intensive industries, the cooperation mechanism under various policies is investigated [45]. Regulation-related research: This study looks at how choosing a digital transformation plan changes over time in renewable energy power plants and sales companies that are governed by the government [46]. Through the evolutionary game, the other research studies the strategic choices of regulators and traditional energy companies and studies how economic penalties affect the strategic choices of participants [47]. To enhance supervisory intensity, whistleblowers are introduced into the evolutionary game, establishing a tripartite model involving regulators, energy companies, and whistleblowers [48]. The other study creates a tripartite evolutionary game model to investigate how media scrutiny and governmental monitoring affect energy companies’ efforts to reduce carbon emission data fraud [49]. Research on resource endowment: In order to look at how water resources affect the main body’s behavior, an evolutionary game model with local government, energy companies, and food producers is built [50]. The other study, which focuses on rural energy, examines the mechanisms of change in the rural energy sector and creates a tripartite evolutionary game model including farmers, new energy companies, and the government [51]. This study explores the relationship between government policies and behavior strategies through a tripartite evolutionary game including firms, the government, and energy regulatory service centers [52]. Research on carbon emissions uses a tripartite evolutionary game combining governments, carbon verification agencies, and high-energy-consuming firms to examine the effect of carbon trading on the low-carbon transformation of businesses [53]. The other study establishes a tripartite evolutionary game model involving local governments and two comparable energy businesses in order to investigate the crucial role that low-carbon technology innovation plays in cutting carbon emissions [54]. Another study creates a two-party evolutionary game model between the government and energy businesses to examine how carbon prices and carbon quotas impact government enterprise behavior [55].

From the literature reviewed above, it is evident that government regulation significantly influences the behavior of energy enterprises and fosters advancements in energy green innovation. In the study of the evolutionary game of energy enterprises, it is impossible to explain the phenomenon that only considering the self-interest preference of energy enterprises will lead to the consistent decision-making results of different research subjects. Many scholars have introduced fairness preference factors in different research fields, such as the supply chain field [56,57], venture capital field [58], PPP project [59,60], enterprise performance [61], major project [62], and regional industrial planning [63]. Considering fairness preference explains the game experimental results and economic behavior that pure self-interest preference cannot explain, and energy enterprises have great social responsibility. Its behavior is also affected by public opinion. As a result, the evolutionary game trend and stability analysis are examined, and the fairness preference factor and reputation are added to the evolutionary game research of energy companies and governments. Finally, the evolutionary characteristics of the subject’s decision-making behavior under different conditions are explained by numerical simulation.

The contribution of this research is found in its investigation of the influence of fairness desires on energy firms’ green innovation. The utility of the fairness preference of energy firms is measured by using their baseline income as a reference point and the excess subsidy or punishment brought about by innovation green. Secondly, the reputation is introduced into the evolutionary game model of energy enterprises and governments to explore the impact of reputation on the green innovation behavior of energy enterprises. Thirdly, the ultimate steady-state strategy decisions made by the government and energy companies are simulated through numerical simulation analysis. This gives the government a guide for rewarding and penalizing green innovation policies and supports its efforts to encourage green innovation in the energy industry.

3. Model Hypothesis and Construction

The selection of variables in this paper refers to the studies of Shi [43], Zhou [44], Yang [48], Huang [64] and Li [65]. The variables are shown in

Table 1. The basic variables in the game model.

Variables	Meaning of Variables	Range
$k$	Fairness preference coefficient of energy enterprises	$k\in [0,1]$
$x$	The possibility of energy enterprises adopting a green innovation strategy	$x\in [0,1]$
$1-x$	The possibility of energy companies not adopting green innovation strategies	$(1-x)\in [0,1]$
$y$	The possibility of the government’s regulatory strategy	$y\in [0,1]$
$1-y$	The possibility of the government adopting a non-regulatory strategy	$(1-y)\in [0,1]$
$R$	Compliance income of energy enterprises	$R>0$
$A$	Government subsidies for energy enterprises after green innovation	$A>0$
$C$	The R&D cost of green innovation in energy enterprises	$C>0$
$G$	The government’s tax revenue on energy companies	$G>0$
$H$	The social benefits brought by green innovation of energy enterprises	$H>0$
$S$	The good social reputation brought by green innovation of energy enterprises	$S>0$
$L$	Environmental loss caused by energy enterprises not carrying out green innovation	$L>0$
$F$	Government supervision costs	$F>0$
$W$	Punishment of energy enterprises without green innovation	$W>0$
$E$	The carbon emission cost saved by energy enterprises without green innovation	$E>0$

.

Hypothesis 1. 

It is assumed that the main body of the evolutionary game is composed of energy enterprises and the government, both of which are bounded rational subjects, which means that all parties in the game can gradually stabilize the strategy selection to the optimal strategy through continuous trial and error and learning. It is assumed that the government is the one who only cares about the maximization of material benefits, while the energy enterprise is the one who prefers to care about the material returns of itself and the government fairly.

Hypothesis 2. 

We use $k$ to represent the fairness preference; the higher the value of $k$, the stronger the fairness preference. The fairness preference of the actor can be divided into two categories: the proud tendency to love their own income higher than the other’s and the jealous tendency to envy the other’s income higher than their own [66,67].

Hypothesis 3. 

The strategic space choice of energy enterprises is (adopt green innovation, no adopt green innovation), choosing to adopt green innovation with the probability of $x$, and choosing not to adopt green innovation with the probability of $1-x$; in order to distinguish whether energy companies adopt green innovation, the government’s strategic space choice is (supervision, no supervision), and chooses supervision with the probability of $y$, and chooses no supervision with the probability of $1-y$.

Hypothesis 4. 

Generally, the economic benefits generated by green innovation of energy enterprises are owned by the government, while the benefits of energy enterprises are obtained through their own income and government subsidies. When an energy enterprise entity adopts a green innovation strategy, the government will initially reward it, but there will be innovation costs involved. Additionally, based on public opinion, there may be non-material benefits such as a positive reputation and future opportunities to work with the government. The government’s tax revenue for energy companies is the social benefit of energy companies choosing green innovation. Therefore, when energy companies do not choose green innovation, they can also obtain additional benefits by saving the cost of carbon emissions. Energy companies that do not adopt green innovation will cause the loss of economic benefits caused by the social environment.

Hypothesis 5. 

The government will supervise the behavior of energy enterprises. After government supervision, it can be found that energy enterprises do not adopt green innovation behavior and will punish energy enterprises. When the government adopts an unsupervised strategy, it will not generate costs and cannot identify the behavior of energy companies.

Based on the hypothesis, the payment matrix of the two parties is constructed as shown in

Table 2. Evolutionary game payoff matrix between government and energy enterprises.

Government		Regulation	No Regulation
Energy enterprise	Adopt	$R+A-k(H-F-A+C)$ $+S-C,G+H-F$	$R+A-k(H-A+C)$ $-C+S,G+H$
	No adopt	$R+E-k(2W-F-L-E)$ $-W,G-F-L+W$	$R+E-k(-L-E),$ $G-L$

.

Based on the table above, the replication dynamic equations for the government and energy enterprises can be derived as follows:

$$F(x)={\displaystyle \frac{dx}{dt}}=x(1-x)[S+A-C-E-k(H-A+C+L+E)+yW(1+2k)]$$

(1)

$$F(y)={\displaystyle \frac{dy}{dt}}=y(1-y)(W-xW-F)$$

(2)

4. Strategy Stability Analysis of Energy Enterprises

According to Formula (1), the derivation of it can result in Formula (3) as follows:

$$F^{\prime }(x)=(1-2x)[S+A-C-E-k(H-A+C+L+E)+yW(1+2k)]$$

(3)

Based on the features of evolutionary stable strategies and the stability theorem of replicator dynamics equations, if $x$ is ESS, it should satisfy $F(x)=0 \mathrm{and} F^{\prime }(x)<0$. When $F(x)=0$, $x=1$ or $x=0$ or $y^{*}={\displaystyle \frac{E+C-S-A+k(H-A+C+L+E)}{W(1+2k)}}$.

When $y={\displaystyle \frac{E+C-S-A+k(H-A+C+L+E)}{W(1+2k)}}$, $F(x)\equiv 0$. At this time, all $x$ are in a stable state, and the strategic choice of energy enterprises will not change with the development of time.

When $y={\displaystyle \frac{E+C-S-A+k(H-A+C+L+E)}{W(1+2k)}}$, if $F(x)=0$, then $x=0$ and $x=1$.

When $y>y^{*}$, $x=1$ is the evolutionary equilibrium point, and the behavior taken by energy enterprises is ‘adopt effort machine behavior’.

When $y<y*$, $x=0$ is the evolutionary equilibrium point, and the behavior adopted by energy enterprises is ‘not adopt green innovation’.

When energy companies adopt green innovation, they will obtain higher subsidies. Energy companies will adopt green innovation. For the government, the probability of government supervision is directly proportional to the benefits of energy companies not adopting green innovation and the cost of energy companies adopting green innovation; the reputation and other non-material benefits obtained by energy companies after adopting green innovation are inversely proportional, and in different scenarios, the probability of government supervision and the strength of fairness preference have different changes. When $H-A+C+L+E>0$, that is, the energy companies take green innovation. The income is small, and the probability of government supervision is proportional to the strength of the fairness preference of energy companies. When $H-A+C+L+E<0$, that is, the benefits brought by green innovation of energy enterprises are large, the probability of government supervision is inversely proportional to the intensity of fairness preference of energy enterprises.

5. The Stability Test of Government Strategy

According to Formula (2), Formula (4) can be obtained by deriving it as follows:

$$F\prime (y)=(1-2y)(W-xW-F)$$

(4)

Based on the features of evolutionary stable strategies and the stability theorem of replicator dynamics equations, if $y$ is ESS, it should satisfy $F(y)=0$ and $F^{\prime }(y)<0$. When $F(y)=0$, $y=1$ or $y=0$ or $x^{*}={\displaystyle \frac{W-F}{W}}$.

When $x=x*,F(y)\equiv 0,W>F$. At this time, all $y$ are in a stable state, and the strategic choice of energy enterprises will not change with the development of time.

When $x\ne x*$, if $F(y)=0$, then $y=0$ and $y=1$.

When $x>x^{*}$, $y=0$ is the evolutionary equilibrium point, and the behavior taken by government is ‘not regulation’.

When $x<x*$, $y=1$ is the evolutionary equilibrium point, and the behavior adopted by government is ‘regulation’.

When the punishment for energy enterprises not to adopt green innovation is large, the probability for the government to adopt supervision is relatively large. For energy companies, the government’s supervision cost also affects the behavior choice of energy companies. When the supervision cost is too high, the probability of energy companies not adopting green innovation is greater. When the government’s supervision cost is low, the probability of energy companies adopting green innovation is greater. The punishment for not adopting green innovation regulations will also affect the behavior choices of energy enterprises. When there is a large penalty for not adopting green innovation regulations, energy corporations are more inclined to adopt green innovation. When there is no chance of punishment for not adopting green innovation, energy corporations are more likely to do so.

6. Equilibrium Point and Stability Analysis of an Evolutionary Game System

By combining the replication dynamic equations of energy enterprises and governments, the stable equilibrium point of the system can be obtained: $E_1(0,0)$ $E_2(0,1)$ $E_3(1,0)$ $E_4(1,1)$ $E_5(x^{*},y^{*})$.

$$J=\left[\begin{array}{cc}{\displaystyle \frac{\partial F(x)}{\partial x}}& {\displaystyle \frac{\partial F(x)}{\partial y}}\\ {\displaystyle \frac{\partial F(y)}{\partial x}}& {\displaystyle \frac{\partial F(y)}{\partial y}}\end{array}\right]$$

(5)

$${\displaystyle \frac{\partial F(x)}{\partial x}}=(1-2x)[S+A-C-E-k(H-A+C+L+E)+yW(1+2k)]$$

(6)

$${\displaystyle \frac{\partial F(x)}{\partial y}}=x(1-x)W(1+2k)$$

(7)

$${\displaystyle \frac{\partial F(y)}{\partial x}}=-y(1-y)W$$

(8)

$${\displaystyle \frac{\partial F(y)}{\partial y}}=(1-2y)(W-xW-F)$$

(9)

The matrix determinant and matrix trajectory are as follows following additional analysis:

$$\det J={\displaystyle \frac{\partial F(x)}{\partial x}}\ast {\displaystyle \frac{\partial F(y)}{\partial y}}-{\displaystyle \frac{\partial F(x)}{\partial y}}\ast {\displaystyle \frac{\partial F(y)}{\partial x}}$$

(10)

$$trJ={\displaystyle \frac{\partial F_1(x)}{\partial x}}+{\displaystyle \frac{\partial F_1(y)}{\partial y}}$$

(11)

For the evolutionary game of two parties, when $\det J>0$ $trJ<0$, the equilibrium point is a stable point.

Based on the four scenarios shown in

Table 3. Stability analysis of equilibrium point.

Local Equilibrium Point	$\mathbf{det}\mathit{J}$	$\mathit{t}\mathit{r}\mathit{J}$
$E_1(0,0)$	$[S-k(H-A+C+L+E)$ $+A-C-E](W-F)$	$S-k(H-A+C+L+E)$ $+A-C-E+(W-F)$
$E_2(0,1)$	$-[S+A-k(H-A+C+L+E)$ $-C-E+W(1+2k)](W-F)$	$S-k(H-A+C+L+E)-E$ $+W(1+2k)+A-C-(W-F)$
$E_3(1,0)$	$[S-k(H-A+C+L+E)$ $+A-C+E]F$	$-S+k(H-A+C+L+E)-F$ $-A+C+E$
$E_4(1,1)$	$-[S-k(H-A+C+L+E)$ $+W(1+2k)+A-C-E]F$	$-[S-k(H-A+C+L+E)$ $+W(1+2k)+A-C-E]+F$

.

Scenario 1: $S+A-C-E>k(H-A+C+L+E)$ and $W>F$. At this time, the subsidy for green innovation behavior of energy enterprises is at a high level, and the government’s supervision cost is less than the government’s punishment for energy enterprises not adopting green innovation. The specific stability analysis is shown in

Table 4. Stability analysis of Scenario 1.

Local Equilibrium Point	$\mathbf{det}\mathit{J}$	$\mathit{t}\mathit{r}\mathit{J}$	Result
$E_1(0,0)$.	+	+	Saddle point
$E_2(0,1)$	−	Undetermined	Saddle point
$E_3(1,0)$	+	−	ESS
$E_4(1,1)$	−	−	Saddle point

.

Scenario 2: $S+A-C-E>k(H-A+C+L+E)$ and $W<F$.

At this time, the subsidy for green innovation behavior of energy enterprises is at a high level, and the government’s supervision cost is greater than the government’s punishment for energy enterprises not adopting green innovation. The specific stability analysis is shown in

Table 5. Stability analysis of Scenario 2.

Local Equilibrium Point	$\mathbf{det}\mathit{J}$	$\mathit{t}\mathit{r}\mathit{J}$	Result
$E_1(0,0)$.	−	Undetermined	Saddle point
$E_2(0,1)$	+	+	Saddle point
$E_3(1,0)$	+	−	ESS
$E_4(1,1)$	−	−	Saddle point

.

Scenario 3: $k(H-A+C+L+E)-W(1+2k)<S+A-C-E<k(H-A+C+L+E)$ and $W<F$.

At this time, the subsidy for green innovation behavior of energy enterprises is at a medium level, and the government’s supervision cost is greater than the government’s punishment for energy enterprises not adopting green innovation. The specific stability analysis is shown in

Table 6. Stability analysis of Scenario 3.

Local Equilibrium Point	$\mathbf{det}\mathit{J}$	$\mathit{t}\mathit{r}\mathit{J}$	Result
$E_1(0,0)$	+	−	ESS
$E_2(0,1)$	+	+	Saddle point
$E_3(1,0)$	−	Undetermined	Saddle point
$E_4(1,1)$	−	Undetermined	Saddle point

.

Scenario 4: $k(H-A+C+L+E)-W(1+2k)>S+A-C-E$ and $W>F$.

At this time, the subsidy for green innovation behavior of energy enterprises is at a low level, and the government’s supervision cost is less than the government’s punishment for energy enterprises not adopting green innovation. The specific stability analysis is shown in

Table 7. Stability analysis of Scenario 4.

Local Equilibrium Point	$\mathbf{det}\mathit{J}$	$\mathit{t}\mathit{r}\mathit{J}$	Result
$E_1(0,0)$.	−	Undetermined	Saddle point
$E_2(0,1)$	+	−	ESS
$E_3(1,0)$	−	Undetermined	Saddle point
$E_4(1,1)$	+	+	Saddle point

.

Scenario 5: $k(H-A+C+L+E)-W(1+2k)>S+A-C-E$ and $W<F$.

At this time, the subsidy for green innovation behavior of energy enterprises is at a medium level, and the government’s supervision cost is less than the government’s punishment for energy enterprises not adopting green innovation. The specific stability analysis is shown in

Table 8. Stability analysis of Scenario 5.

Local Equilibrium Point	$\mathbf{det}\mathit{J}$	$\mathit{t}\mathit{r}\mathit{J}$	Result
$E_1(0,0)$	+	−	ESS
$E_2(0,1)$	−	Undetermined	Saddle point
$E_3(1,0)$	−	Undetermined	Saddle point
$E_4(1,1)$	+	+	Saddle point

.

This paper obtains four evolutionary stable points of government and energy enterprises and under what scenarios they reach stability. The specific situation is shown in

Table 9. Stability analysis.

Local Equilibrium Point	Point of Equilibrium	Strategy Selection	Validity
Scenario 1	$E_3(1,0)$	(Green innovation, Not regulation)	most ideal
Scenario 2	$E_3(1,0)$	(Green innovation, Not regulation)	most ideal
Scenario 3	$E_1(0,0)$	(Not green innovation, Not regulation)	non-ideal
Scenario 4	$E_2(0,1)$	(Not green innovation, Regulation)	most low ideal
Scenario 5	$E_1(0,0)$	(Not green innovation, Not regulation)	non-ideal

. The most ideal situation is that energy companies adopt green innovation strategies while the government does not need supervision. The least ideal situation is that the government adopts a regulatory strategy and energy companies do not adopt green innovation strategies.

7. Simulation Analysis

In order to verify the fairness preference of energy enterprises and the government’s green innovation behavior of energy enterprises, as well as the impact of the government’s punishment for energy enterprises not adopting green innovation on the behavior of energy enterprises, this paper uses MATLAB R2022 a to simulate and analyze the energy enterprises and the government within the reasonable parameters. The specific values are shown in

Table 10. Parameter assignment of evolutionary game stable strategy.

	S	A	C	E	k	H	W	F	L
Scenario 1	2	12	4	5	0.3	5	3	2	2
Scenario 2	2	12	4	5	0.3	5	2.5	3	2
Scenario 3	2	10	4	5	0.8	7	1.5	2	3
Scenario 4	2	5	4	5	0.3	12	4	3.5	2
Scenario 5	2	7	4	5	0.3	10	1.5	2	3

.

Figure 1 shows the eight sets of initial strategy combinations randomly generated in five scenarios and the behavior choices made by energy companies and governments after a period of time to reach a stable state.

7.1. The Impact of Energy Companies ‘Fairness Preference on Energy Companies’ Strategic Choice

In order to study the influence of fair preference of energy enterprises on the behavior choice of energy enterprises, this study assumes that other constraints remain unchanged and only changes the parameter values of fair preference of energy enterprises to k = 0.1, 0.2, 0.3, 0.5, 0.7, and 0.8. Through the analysis of the results of Figure 2 below, it can be seen that the fair preference of energy enterprises has an impact on the behavior choice of energy enterprises. In the case of k = 0.1, 0.2, and 0.3, energy enterprises adopt green innovation, while in the case of k = 0.5, 0.7, and 0.8. Energy companies do not adopt green innovation. It can be seen that an energy company with strong fairness preference is more likely to adopt green innovation because an energy company with strong fairness preference will compare its own income with the government’s income. He pays more attention to his own income rather than the overall income, while an energy company with weak fairness preference is more likely to adopt green innovation, and he will sacrifice some personal interests for the overall income. Therefore, identifying the fairness preference of energy enterprises can choose a reasonable way to prevent energy enterprises from not adopting green innovation to a greater extent for the government. In practice, the government chooses research reports and financial data to predict the fairness preference of energy enterprises in the bidding of many energy enterprises.

7.2. The Impact of Government Subsidies on the Strategic Choice of Energy Enterprises

When the fairness preference is not considered, assuming that other constraints remain unchanged, the income value A obtained by energy enterprises in the adjustment model when adopting green innovation is set to 6, 8, 10, 12, 14, and 16. Analysis of the results of Figure 3 shows that the more government subsidies energy enterprises receive from green innovation, the greater the probability that energy enterprises adopt green innovation, the less rewards they receive, and the greater the probability that energy enterprises do not adopt green innovation. In general, if energy enterprises can obtain more government subsidies, energy enterprises will be more likely to choose green innovation.

When considering the fairness preference, it is assumed that the fairness preference coefficient of energy enterprises and government subsidies change together. According to the analysis of the results of Figure 4, the fairness preference of energy enterprises will show different choice behaviors. When the government subsidies obtained by energy enterprises are low, energy enterprises with weak fairness preference tend to choose green innovation, and energy enterprises with strong fairness preference tend to choose not to adopt green innovation. Only when energy enterprises obtain higher government subsidies, regardless of the fairness preference of energy enterprises, will they choose green innovation.

7.3. The Impact of Government Punishment on the Strategy of Energy Enterprises

The government punishment here refers to the punishment measures when the government policy does not adopt green innovation for energy enterprises. When the fairness preference is not considered, assuming that other constraints remain unchanged, the penalty value W obtained by the energy enterprises in the adjustment model when they do not adopt green innovation is set to 0.5, 1.5, 7, and 10, respectively. The analysis of the results in Figure 5 shows that government punishment can limit the energy enterprises from not adopting green innovation. The higher the loss caused by punishment to energy enterprises, the greater the probability of energy enterprises adopting green innovation.

It is believed that when taking into account the fairness preference, changes in the government penalty and the fairness preference of energy enterprises will occur simultaneously. Based on the examination of Figure 6, it can be inferred that energy enterprises with lower fairness preferences are more likely to adopt green innovation when it is not adopted with less punishment, whereas those with higher fairness preferences are less likely to do so. Regardless of the energy firms’ preference for fairness, they will not choose to adopt green innovation until they face penalties from the government.

7.4. The Impact of Reputation on the Strategy of Energy Enterprises

Reputation refers to the good social evaluation brought by energy enterprises after taking social responsibility, which is the intangible income of enterprises. When the fairness preference is not considered, it is assumed that other constraints remain unchanged, and the reputation obtained by energy companies adopting green innovation in the adjustment model is set to 1, 1.5, 2, 4, 4.5, and 5, respectively. The analysis of the results in Figure 7 below shows that reputation helps energy companies adopt green innovation behavior.

When considering fairness preference, it is assumed that the fairness preference and reputation of energy companies change together. According to the results of Figure 8, when energy companies have less reputation, energy companies with weaker fairness preferences tend to choose green innovation, while energy companies with stronger fairness preferences tend to choose not to adopt green innovation. When energy companies have a greater reputation, they will choose green innovation regardless of the fairness preference of energy companies.

8. Discussions

The green innovation behavior of energy enterprises plays an important role in environmental protection and social development. The government’s regulatory strategy has an important impact on the green innovation behavior choice of energy enterprises. The research in this paper mainly focuses on the green innovation behavior of energy enterprises and constructs a two-party evolutionary game model of government and energy enterprises. This model combines the fairness preference of energy enterprises, studies the influence of the fairness preference of enterprises, the government’s subsidy and punishment regulation strategy, and social reputation on the green innovation behavior of energy enterprises, and verifies the obtained results through simulation analysis. This study enriches the research on the green innovation behavior of energy enterprises and provides valuable insights for the government to promote the sustainable development of the energy industry.

In the model analysis, this paper combines the fairness preference of energy enterprises with the evolutionary game model and transforms the traditional economic hypothesis into the social man hypothesis. At the same time, considering that the social attributes of enterprises introduce the influence factor of reputation, the research results are more in line with reality. First of all, this study verifies that under the traditional economic man hypothesis, the government’s regulatory strategy will promote the green innovation behavior of energy enterprises [68]. If the government’s subsidies are large, there will be a greater probability that energy companies will choose green innovation; when the government does not adopt green innovation for energy companies, it will be subject to greater penalties, which can well promote energy companies to adopt green innovation [7]. Yunneng Technology was fined by the Environmental Protection Agency for illegal discharge of wastewater in 2020. Subsequently, the company upgraded the technology, improved the wastewater treatment system, and promoted the development of the enterprise [52]. Verifying reputation can promote green innovation behavior of energy companies [69]. The social reputation of energy companies has a huge impact on their future sustainable development [70]. As Xiexin integrated energy enterprises through innovative activities, in the realization of enterprise value at the same time, continue to assume social responsibility to achieve business value, brand value, and strategic value of the great breakthrough [71]. Secondly, after considering the fairness preference, this paper finds that the fairness preference of energy enterprises will affect the green innovation behavior of energy enterprises. At the same time, it will also cooperate with the government’s subsidy and punishment strategies for energy enterprises and reputation to affect the green innovation behavior of energy enterprises. Compared with previous studies, after considering fairness preference, the threshold for energy enterprises to choose green innovation is reduced. As in the previous simulation analysis, when the government’s subsidy to energy enterprises is 10, energy enterprises will not choose green innovation behavior without considering fairness preference. Under the same subsidy strategy, when the fairness preference of energy enterprises is 0.3, energy enterprises will finally choose green innovation behavior. When the fairness preference of energy enterprises is 0.8, although energy enterprises will not choose green innovation behavior in the end, it slows down the speed of not choosing green innovation behavior. The synergy between the fairness preference of energy enterprises and the government’s punishment strategy and reputation on the green innovation behavior of energy enterprises is similar to the synergy between the fairness preference of energy enterprises and the government subsidy strategy on the green innovation behavior of energy enterprises. The fairness preference found in the field of supply chain [57] and PPP project [59] can affect decision-making by changing its own utility. This study verifies the important role of fairness preference in the field of energy enterprises. Thirdly, compared with the previous research on the government’s incentive strategy for energy enterprises, previous studies have found that the punishment for energy enterprises ‘non-choice of green innovation behavior is stronger than the subsidy for energy enterprises’ green innovation behavior [54]. However, through the analysis of Scenario 1 and Scenario 2, this paper finds that increasing the subsidy for energy enterprises’ green innovation behavior considering fairness preference can make energy enterprises more inclined to choose green innovation behavior. Finally, the study found that energy companies with strong fairness preferences have a relatively high probability of not adopting green innovation. In the process of green innovation, more subsidies are needed to perceive fairness. Such energy companies are more concerned with personal interests rather than collective interests. When they perceive that they are unfairly treated, energy companies will choose not to adopt green innovation regardless of whether the government chooses to regulate or not. Energy companies with weaker fairness preferences have a higher probability of adopting green innovation. Although they have only received less income in the process of income distribution, they will choose to adopt behaviors that are conducive to collective interests. Such energy companies are more concerned with long-term interests rather than short-term interests. Therefore, the government needs to adopt different regulatory strategies for different energy companies. It is of great significance to study the government regulation strategy to promote the green innovation behavior of energy enterprises.

9. Conclusions

Through the analysis of the behavior of energy enterprises and the government, this paper analyzes the behavior of energy enterprises and the government. In the case of fair preference of energy enterprises, when energy enterprises adopt a certain behavior, energy enterprises will pay attention to the benefits and losses brought by this behavior to energy enterprises themselves and pay attention to the benefits or losses brought to the government because of their own fair preference. The stability strategies of the government and energy enterprises in different situations are studied. Finally, the game results are obtained, and the game results are simulated and analyzed. The conclusions are as follows:

Under certain conditions, the evolutionary game model in this paper has five stable states and three ESS $E_1(0,0)$ $E_2(0,1)$ $E_3(1,0)$, among which $E_3(1,0)$ is the most ideal and $E_2(0,1)$ is the least ideal. The government’s subsidy policy plays a leading role in promoting energy companies to choose the most ideal situation, and the government’s punishment strategy mainly affects the government’s regulatory strategy choice.

External factors such as government subsidies, punishment, and social reputation will affect the choice of green innovation behavior of energy enterprises. The greater the value of these external factors, the higher the probability that energy enterprises tend to green innovation behavior.

Fairness preference is a key internal factor affecting the choice of green innovation behavior of energy enterprises. An energy enterprise with strong fairness preference is more likely to not adopt green innovation behavior. Contractors with weaker fairness preferences are more likely to adopt green behavior innovation. Secondly, under the government subsidy and punishment policy, energy enterprises with high fairness preferences need higher punishment and subsidy to choose green innovation behavior; energy companies with low fairness preferences will choose green innovation behavior with lower subsidies and penalties. Third, the reputation of energy companies helps energy companies adopt green innovation behavior. Due to the different fairness preferences of energy companies, the role of reputation mechanisms is not the same. Energy companies with weaker fairness preferences pay attention to the public interest, and the reputation mechanism has a stronger effect. Based on the research of this paper, the following suggestions are made for the government to promote green innovation behavior of energy enterprises.

First, classify energy companies according to fairness preferences. The government classifies energy enterprises. For different energy enterprises, their economic status and scale of development are different, and their needs for fairness are also different. Therefore, different types of energy enterprises need to be subsidized and punished to varying degrees. The government divides the fairness preference of energy enterprises through the financial data and research reports of energy enterprises and adopts different subsidy and punishment strategies for different levels of polluting enterprises. Solve the problem that energy companies will make different behavioral decisions for the same government policy and actively guide energy companies to adopt green innovation behavior.

Second, the government’s regulatory strategy for green innovation behavior of energy enterprises focuses on subsidies for green innovation behavior of energy enterprises. This strategy is not only to reduce the economic pressure faced by energy enterprises in the process of transformation but also to accelerate the development and promotion of green technology. Through financial subsidies, the government can reduce the cost of green innovation to a certain extent, so as to encourage more enterprises to invest resources in the development of environmental protection technology. In addition, this subsidy policy also helps to shorten the conversion time of new technologies from the laboratory to the market, enabling green technologies to achieve commercial applications faster.

Third, the government guides energy companies to attach importance to the role of corporate reputation in green innovation. The government needs to guide energy companies to correctly understand the great value of green innovation for enterprises and promote energy companies to increase investment in R&D and innovation; at the same time, through the supervision of public opinion, the energy enterprises can clarify their social responsibilities, encourage energy enterprises to actively undertake their social responsibilities, and respond to the supervision of public opinion. The government formulates policies for green innovative technologies that are suitable for the development of energy enterprises and realizes the unity of economic development and environmental protection.

There are also some limitations in the research of this paper. Firstly, the subjects of the evolutionary game in this study are only the government and energy companies, while in practice, there are other third parties besides the government and companies. Secondly, the fairness preference in this study is only targeted at energy companies, and in practice, not only energy companies but also governments have fairness preferences. Finally, this study only examined the government’s subsidy and punishment strategies for energy companies at the macro level, and further research can be conducted at the micro level in the future.