Understanding the Intersection of Central Environmental Protection Inspections and Green Investment Through Game Theory

Abstract

The Central Environmental Protection Inspector (CEPI) is an innovation in China’s environmental regulation. This paper uses game theory to analyze the influence of the CEPI on enterprises’ green investment. Firstly, by constructing the game model of “central government-local government-polluting enterprises”, the factors affecting green investment strategy are analyzed. Then, with the help of a system simulation model, the influence of parameters on system stability and convergence trends is analyzed, so as to obtain the influence of the CEPI on enterprise green investment. The results show the following: (1) The CEPI can effectively promote preventive green investment, and the promotion effect of preventive green investment is proportional to its risk; (2) The effect of the CEPI on local governments is not obvious; (3) The cost of the CEPI is too high, and polluting enterprises are quick to choose remedial green investment.

1. Introduction

Since the reform and opening up, China’s economy has achieved rapid growth. However, the high input, high consumption, and high emission growth model has led to a series of problems such as overcapacity, resource shortages, and environmental pollution [1]. Authorities want to decouple economic growth from carbon emissions and environmental damage [2] and accelerate the green transformation of development modes. Enterprises, especially those heavily polluting ones, are the main consumers of resources, major emitters of pollution, and also the primary practitioners of green transformation [3,4]. To achieve greener socio-economic development, there are certainly higher demands on micro-level enterprises for green investments and clean production. Therefore, exploring how enterprises adjust their green investment strategies to achieve corporate green transformation is of great significance for the sustainable development of China’s economy.

Corporate green investment refers to the investment behavior of companies aiming at implementing green management and reducing environmental risks, by allocating funds to prevent and control environmental pollution [5,6]. Depending on the purpose of the investment funds, green investments are further divided into preventive green investments and remedial green investments [7,8,9]. Specifically, preventive green investments involve companies investing in clean energy, improving clean production processes, and developing environmental protection technologies. Remedial green investments mainly refer to companies using funds to address existing environmental pollution without changing their current production methods. Both types of green investments can reduce pollution emissions to some extent and enhance the “greening” level of enterprises. However, there are clear differences between them in terms of their nature and objectives. End-of-pipe remedial green investments require less capital, have lower uncertainty, and can help companies meet current government environmental regulations in a short period. However, this is merely a symptomatic solution for companies dealing with environmental governance. In contrast, preventive green investments aim to reduce pollution emissions while enhancing overall productivity by seeking clean energy sources, innovating clean production processes, and developing green technologies. This is a fundamental strategy for companies to achieve green transformation and upgrading. However, preventive green investments have characteristics such as strong externalities, long cycles, high costs, and significant risks, bringing uncertainty to corporate profits [10]. In the case of an enterprise’s investment in an electric vehicle charging infrastructure, the market acceptance risk is a concern. If the adoption rate of electric vehicles in the target area is slower than anticipated due to factors like a lack of consumer incentives or limited availability of electric vehicle models, the revenue generated from the charging facilities may not meet expectations, leading to a less favorable return on investment. Therefore, profit-driven companies are not very willing to actively adopt preventive green investments. Mariz and Savoia’s research show that prevention represents just 7% of sustainable finance in a large emerging market such as Brazil [11].

The central government has implemented a suite of policies aimed at encouraging enterprises to undertake preemptive green investments. Despite these initiatives, local governments have been observed to partially fail in policy execution [12] and to engage in collusive practices with businesses, resulting in suboptimal policy enforcement [13]. In response to these central–local discrepancies, the Central Environmental Protection Inspector (CEPI) has been instituted. Facing the CEPI, how will enterprises make green investment decisions? Will they adopt preventive green or remedial green investments? What reasons will affect the investment strategy choice of the enterprise? The evolutionary game model can dynamically show the evolution of an enterprise’s strategy over time and consider the strategy choices of enterprises that change due to income and experience under environmental supervision, so as to accurately analyze enterprise behavior [14,15]. This paper takes the CEPI as the implementation background, constructs an evolutionary game model of “central government—local government—polluting enterprises”, and studies the above issues.

The remainder of this study is organized as follows. Section 2 reviews the policy background and briefly discusses the literature on the CEPI and green investment. We then set up a three-party game model of “central government-local government-polluting enterprises” in Section 3. Section 4 analyzes the strategic stability and system equilibrium points of different entities and then obtains the stability of enterprises’ green investment strategy selection under the CEPI. Section 5 uses the system simulation model to describe the influence of the main parameters on the stability and convergence trend of the system and analyzes the factors affecting the effect of the CEPI. Last, we offer our main conclusion and policy implications in Section 6.

2. Policy Background and Literature Review

After an initial trial in the Hebei Province of China in January 2016, a central environmental inspection team, consisting of representatives from the Ministry of Environmental Protection, the Organization Department of the Central Committee of the Communist Party of China, and the Central Commission for Discipline Inspection, conducted a series of inspections across 30 provinces and municipalities from June 2016 to September 2017. The inspections prioritized the assessment of critical environmental issues and their resolution, the lack of action and improper conduct in environmental management by local party committees and governments along with their associated departments, and the enforcement of environmental protection responsibilities [16]. These environmental inspections function as a dual mechanism, overseeing both enterprises and governance: they have not only revealed instances of data falsification in pollution monitoring by local enterprises but have also prompted local governments to take the lead in overseeing corrective actions.

The CEPI represents a significant reform in China’s environmental regulatory policy expanding the structure of China’s environmental governance and promoting the development of China’s environmental governance model from “government management” to a multi-faceted governance model involving “central government—inspection team—local government—enterprises—public” [17], which has had certain impacts on local government’s environmental governance behavior, corporate behavior, and pollution emissions. The research on the CEPI mainly focuses on how it affects local government regulation, corporate behavior, and air pollution. In terms of the impact of the CEPI on local governments, Yuan and Yang found that the implementation of the CEPI effectively reduced information asymmetry in the “central-local” vertical principal–agent relationship [18]. Zhuang et al. found that the CEPI prompted grassroots governments and environmental protection departments to adjust their organizational structures, changing the originally weak image of the environmental protection departments and expanding their authority [19]. Regarding the impact of the CEPI on corporate behavior, some scholars pointed out that the CEPI can prompt heavily polluting enterprises to change production decisions [20], induce corporate innovation [21], and improve corporate environmental performance [22]. In terms of the impact of the CEPI on pollution control, Liu et al. found through empirical research that the CEPI can temporarily improve the air quality of the inspected areas, but after the inspection team leaves, pollution may even rebound [23]. The studies by Zeng et al. and Kou et al. show that the CEPI effectively promotes regional green transformation by reducing local pollution emissions and improving total factor productivity [16,24].

Indeed, environmental regulation is widely acknowledged by global researchers as a critical factor for regional green transformation and governance. Dzwigol et al. noted that within the European Union member states, environmental regulation, renewable energy, and energy efficiency are pivotal in fostering green economic growth [25]. Khaddage-Soboh et al. examined the significant role of natural resource rents, environmental regulations, and environmental taxes in promoting sustainable development in G7 countries, emphasizing the importance of a robust regulatory framework [26]. Ahmad et al. conducted a study across 26 European Union member states and concluded that environmental regulations serve as an effective monitoring and control mechanism, significantly reducing CO₂ emissions [27].

Among the existing research results, there is no direct discussion on the impact of the CEPI on enterprises’ green investment behavior. However, corporate green investment is a direct manifestation of corporate environmental governance, so examining the impact of the CEPI on green investment is very important to understanding the institutional environmental regulation effect. Therefore, we try to analyze the effect of the CEPI on enterprise green investment through game theory and provide theoretical reference for policy makers.

3. Model Assumptions and Evolutionary Game Model Construction

3.1. Model Assumptions

In the process of corporate regulation, there exists a certain tension between the central policy decision-making and local government implementation, with both sides exhibiting a repeated game relationship [28]. Central environmental inspections have evolved from non-existence to pilot exploration and then to full implementation by clarifying the primary responsibility for pollution control, thereby forming a deterrent warning to local governments. The relationship between central government, local government, and business exists as shown in Figure 1.

Taking local governments and polluting enterprises as research subjects, this paper proposes the following basic assumptions for the evolutionary game model:

(1)

Action Strategy Assumption. The central government chooses to inspect or not inspect the local government’s enforcement of environmental regulations, with strategy sets being (Inspection, Non-Inspection). Local governments are responsible for the behavior of polluting enterprises, with strategy sets being (Regulation, Non-Regulation). Polluting enterprises, under the pressure of central environmental inspections, need to meet pollution emission standards and must make green investments, with strategy sets being (Preventive Green Investment, Remedial Green Investment). In the initial stage, the probability of the central government choosing inspection is x, the probability of the local government choosing supervision is $y$, and the probability of polluting enterprises choosing preventive green investment is $z$. Therefore, their probabilities of choosing not to inspect, not to supervise, and remedial green investment are $1-x$, $1-y$, and $1-z$, respectively; x, y, $z\in \left[0,1\right]$, all are functions of time $T$. It is assumed that under the normalization of environmental inspections, enterprises cannot choose not to engage in green investments; otherwise, they will face significant penalties.

(2)

Rationality Assumption of the Main Body. By calculating the costs and benefits of action strategies and combining them with responses to target deviations through adaptation, imitation, or learning, local governments and polluting enterprises exhibit characteristics of bounded rationality in game theory.

(3)

Game Payoff Hypothesis. The payoff matrix of the central government, local government, and polluting enterprises in the air pollution control game is composed of their net benefits (benefit–cost).

For the central government, the tax rate imposed on enterprises is $t$, where 0$<t<1$. This corresponds to various forms of taxes, fees, or transfer payments in reality. After collecting the taxes, the central government allocates a share $\alpha$ to local governments, where 0$<\alpha <1$. The cost for the central government to conduct environmental inspections is $C_a$.

If the central government carries out environmental inspections and local governments regulate enterprises, the probability of detecting excessive pollution emissions by enterprises is δ₁. However, if local governments do not regulate enterprises, the probability of detecting excessive pollution emissions is $\delta$₂, with the condition that 1$>{\delta }_1>{\delta }_2>0$. If excessive pollution is detected, the penalties imposed on local governments and enterprises are $F_{ab}$ and $F_{ac}$, respectively.

For local governments, the cost of regulating enterprises is $C_b$. Local governments receive a tax share from the central government. If the local government does not regulate the enterprise, it can additionally receive benefits transferred from the enterprise, $\beta \left(I_1-I_2\right)$, where 0$<\beta <1$. However, if the enterprise is found by the central government to have excessive pollution emissions, the local government will be penalized $F_{ab}$, and $F_{ab}>\beta \left(I_1-I_2\right)$. If the local government regulates the enterprise and finds that it has excessive pollution emissions, the penalty for the enterprise is $F_{bc}$.

For polluting enterprises, the return on preventive green investment is $R_1$, and the return on remedial green investment is $R_2$. The expenditure on preventive green investment is $I_1$, and there is a risk associated with preventive green investment, with a probability of failure being $\lambda$, where 0 $<\lambda <1$. The expenditure on remedial green investment is $I_2$. Compared to preventive green investment, remedial green investment will produce excessive pollution during non-inspection periods. If the pollution is detected, it faces a fine $F_{ac}$ from the central authority. If the local government chooses to supervise and discovers that the enterprise has pollutant emissions, it imposes a penalty $F_{bc}$ on the enterprise.

The detailed explanations of each parameter in the above assumptions are shown in

Table 1. Parameter Description.

Parameters	Explanations
$R_1$	Returns on preventive green investments by polluting firms
$R_2$	Returns on curative green investments by polluting firms
$I_1$	Expenditure on preventive green investments by polluting firms
$I_2$	Expenditure on curative green investments by polluting firms
$F_{ab}$	Penalties for local governments by the central government for excessive pollution by enterprises
$F_{ac}$	Penalties for polluting enterprises by the central government for excessive pollution
$F_{bc}$	Penalties for polluting enterprises by local governments for excessive pollution
$C_a$	Costs of central government environmental inspections
$C_b$	Costs of local government regulation
$t$	Central government’s tax rate on enterprises
$\alpha$	Central government’s tax revenue sharing with local governments
$\delta$1	Probability of central government detecting excessive pollution by enterprises when local governments regulate
${\delta }_2$	Probability of central government detecting excessive pollution by enterprises when local governments do not regulate
$\beta$	Sharing ratio of information rents between local governments and enterprises
$\lambda$	Risk ratio of enterprises undertaking preventive investments

.

3.2. Evolutionary Game Construction

According to the above description and research hypothesis, the payoff matrix of the central government, local government, and polluting enterprises is shown in

Table 2. “Central Government Local Government Polluting Enterprises” Game Benefit Matrix.

Polluting Enterprises	Central Government Inspection (x)		The Central Government Does Not Supervise (1 − x)
	Local Government		Local Government
	Supervise (y)	Not Regulated (1 − y)	Supervise (y)	Not Regulated (1 − y)
Preventive green investment ($z$)	$A_{111}$	$A_{121}$	$A_{211}$	$A_{221}$
	$B_{111}$	$B_{121}$	$B_{211}$	$B_{221}$
	$C_{111}$	$C_{121}$	$C_{211}$	$C_{221}$
Governance-oriented green investment ($1-z$)	$A_{112}$	$A_{122}$	$A_{212}$	$A_{222}$
	$B_{112}$	$B_{122}$	$B_{212}$	$B_{222}$
	$C_{112}$	$C_{122}$	$C_{212}$	$C_{222}$

.

The benefits of different combinations of game strategies in the game matrix are as follows:

$$\begin{gathered} A_{111}=\left(1-\alpha \right)t{R}_1-C_a+\lambda {\delta }_1\left(F_{ab}+F_{ac}\right) \\ {A}_{112}=\left(1-\alpha \right)t{R}_2-C_a+{\delta }_1\left(F_{ab}+F_{ac}\right) \\ {A}_{121}=\left(1-\alpha \right)t{R}_1-C_a+\lambda {\delta }_2\left(F_{ab}+F_{ac}\right) \\ {A}_{122}=\left(1-\alpha \right)t{R}_2-C_a+{\delta }_2\left(F_{ab}+F_{ac}\right) \\ {A}_{211}=\left(1-\alpha \right)t{R}_1 \\ {A}_{212}=\left(1-\alpha \right)t{R}_2 \\ {A}_{221}=\left(1-\alpha \right)t{R}_1 \\ {A}_{222}=\left(1-\alpha \right)t{R}_2 \\ {B}_{111}=\alpha t{R}_1-C_b+\lambda \left(F_{bc}-{\delta }_1{F}_{ab}\right) \\ {B}_{112}=\alpha t{R}_2-C_b+F_{bc}-{\delta }_1{F}_{ab} \\ {B}_{121}=\alpha t{R}_1+\beta (I_1-I_2)-\lambda {\delta }_2{F}_{ab} \\ {B}_{122}=\alpha t{R}_2+\beta (I_1-I_2)-{\delta }_2{F}_{ab} \\ {B}_{211}=\alpha t{R}_1-C_b+\lambda F_{bc} \\ {B}_{212}=\alpha t{R}_2-C_b+F_{bc} \\ {B}_{221}=\alpha t{R}_1+\beta (I_1-I_2) \\ {B}_{222}=\alpha t{R}_2+\beta (I_1-I_2) \\ {C}_{111}=\left(1-t\right)R_1-I_1-\lambda {\delta }_1{F}_{ac}-\lambda F_{bc} \\ {C}_{112}=\left(1-t\right)R_2-I_2-{\delta }_1{F}_{ac}-F_{bc} \\ {C}_{121}=(1-t)R_1-I_1-\beta (I_1-I_2)-\lambda {\delta }_2{F}_{ac} \\ {C}_{122}=(1-t)R_2-I_2-\beta (I_1-I_2)-{\delta }_2{F}_{ac} \\ {C}_{211}=\left(1-t\right)R_1-I_1-\lambda F_{bc} \\ {C}_{212}=\left(1-t\right)R_2-I_2-F_{bc} \\ {C}_{221}=(1-t)R_1-I_1-\beta \left(I_1-I_2\right) \\ {C}_{222}=(1-t)R_2-I_2-\beta (I_1-I_2) \end{gathered}$$

According to the side matrix of the game subject, the expected returns and average expected returns of the central government’s choice of inspection and non-inspection are, respectively, recorded as $U_{x1}$, $U_{x2}$, and ${\overline{U}}_x$:

$$\begin{gathered} U_{x1}=yz{A}_{111}+y\left(1-z\right)A_{112}+\left(1-y\right)z{A}_{121}+(1-y)(1-z)A_{122} \\ {U}_{x2}=yz{A}_{211}+y\left(1-z\right)A_{212}+\left(1-y\right)z{A}_{221}+(1-y)(1-z)A_{222} \\ {\overline{U}}_x=x{U}_{x1}+(1-x)U_{x2} \end{gathered}$$

The dynamic equation for the central government to choose the strategy of environmental inspection is as follows:

$$\begin{gathered} F\left(x\right)={\displaystyle \frac{dx}{dT}}=x\left(U_{x1}-{\overline{U}}_x\right)=x\left(1-x\right)[\left(F_{ab}+F_{ac}\right)\left(z\lambda -z+1\right)(y{\delta }_1-y{\delta }_2+ \\ {\delta }_2)-C_a] \end{gathered}$$

(1)

Similarly, the expected returns and average expected returns of local governments choosing to regulate and not regulate are recorded as $U_{y1}$, $U_{y2}$, and ${\overline{U}}_y$:

$$\begin{gathered} U_{y1}=xz{B}_{111}+x\left(1-z\right)B_{112}+\left(1-x\right)z{B}_{211}+(1-x)(1-z)B_{212} \\ {U}_{y2}=xz{B}_{121}+x\left(1-z\right)B_{122}+\left(1-x\right)z{B}_{221}+(1-x)(1-z)B_{222} \\ {\overline{U}}_y=y{U}_{y1}+(1-y)U_{y2} \end{gathered}$$

The replication dynamic equation for local governments to choose regulatory strategies is as follows:

$$\begin{gathered} F\left(y\right)={\displaystyle \frac{dy}{dT}}=y\left(U_{y1}-{\overline{U}}_y\right)=y\left(1-y\right)[x\left({\delta }_1-{\delta }_2\right)\left(z-z\lambda -1\right)F_{ab}+ \\ \left(z\lambda -z+1\right)F_{bc}-C_b-\beta (I_1-I_2)] \end{gathered}$$

(2)

The expected returns and average expected returns of polluting enterprises choosing preventive green investment and governance green investment are, respectively, recorded as $U_{z1}$, $U_{z2}$, and ${\overline{U}}_z$:

$$\begin{gathered} U_{z1}=xy{C}_{111}+x\left(1-y\right)C_{121}+\left(1-x\right)y{C}_{211}+(1-x)(1-y)C_{221} \\ {U}_{z2}=xy{C}_{112}+x\left(1-y\right)C_{122}+\left(1-x\right)y{C}_{212}+(1-x)(1-y)C_{222} \\ {\overline{U}}_z=z{U}_{z1}+(1-z)U_{z2} \end{gathered}$$

The replication dynamic equation for polluting enterprises to choose preventive green investment is as follows:

$$\begin{gathered} F\left(z\right)={\displaystyle \frac{dz}{dT}}=z\left(U_{z1}-{\overline{U}}_z\right)=z\left(1-z\right)[x\left(1-\lambda \right)\left(y{\delta }_1-y{\delta }_2+{\delta }_2\right)F_{ac}+ \\ y\left(1-\lambda \right)F_{bc}+\left(1-t\right)\left(R_1-R_2\right)+(I_1-I_2)] \end{gathered}$$

(3)

4. Stability Analysis of Evolutionary Game Theory

This section contains a stability analysis of hybrid strategies for three-dimensional dynamic systems. When the replication dynamic equation of the three parties is zero, the strategies of the three parties in the game system will not change over time and reach a stable equilibrium state of the system. According to the Lyapunov stability theory, when all eigenvalues of the Jacobian matrix are negative, this equilibrium point is the evolutionarily stable point.

By setting $F\left(x\right)=0,F\left(y\right)=0,F\left(z\right)=0$, the local points of a pure policy system can be obtained, namely, $E_1\left(0,0,0\right), E_2\left(0,0,1\right)$, $E_3\left(0,1,0\right), E_4\left(1,0,0\right), E_5\left(0,1,1\right),$ $E_6\left(1,0,1\right), E_7\left(1,1,0\right)$, and $E_8\left(1,1,1\right)$. The corresponding characteristic values are shown in

Table 3. The Corresponding Characteristic Values.

Equilibrium Point	Eigenvalue
	${\mathit{n}}_1$	${\mathit{n}}_2$	${\mathit{n}}_3$
$E_1\left(0,0,0\right)$	${\delta }_2\left(F_{ab}+F_{ac}\right)-C_a$	$F_{bc}-C_b-\beta (I_1-I_2)$	$I_1-I_2+(1-t)\left(R_1-R_2\right)$
$E_2\left(0,0,1\right)$	${\lambda \delta }_2\left(F_{ab}+F_{ac}\right)-C_a$	$\lambda F_{bc}-C_b-\beta (I_1-I_2)$	$-I_1+I_2-(1-t)\left(R_1-R_2\right)$
$E_3\left(0,1,0\right)$	${\delta }_1\left(F_{ab}+F_{ac}\right)-C_a$	${-F}_{bc}+C_b+\beta (I_1-I_2)$	$I_1-I_2+\left(1-t\right)\left(R_1-R_2\right)+(1-\lambda )F_{bc}$
$E_4\left(1,0,0\right)$	$-{\delta }_2\left(F_{ab}+F_{ac}\right)+C_a$	$F_{bc}-C_b-\beta \left(I_1-I_2\right)-({\delta }_1-{\delta }_2)F_{ab}$	$I_1-I_2+\left(1-t\right)\left(R_1-R_2\right)+{\delta }_2(1-\lambda )F_{bc}$
$E_5\left(0,1,1\right)$	${\lambda \delta }_1\left(F_{ab}+F_{ac}\right)-C_a$	$-\lambda F_{bc}+C_b+\beta (I_1-I_2)$	$-I_1+I_2-\left(1-t\right)\left(R_1-R_2\right)-(1-\lambda )F_{bc}$
$E_6\left(1,0,1\right)$	${-\lambda \delta }_2\left(F_{ab}+F_{ac}\right)+C_a$	$\lambda F_{bc}-C_b-\beta \left(I_1-I_2\right)-\lambda ({\delta }_1-{\delta }_2)F_{ab}$	$-I_1+I_2-\left(1-t\right)\left(R_1-R_2\right)-{\delta }_2(1-\lambda )F_{bc}$
$E_7\left(1,1,0\right)$	$-{\delta }_1\left(F_{ab}+F_{ac}\right)+C_a$	$-F_{bc}+C_b+\beta \left(I_1-I_2\right)+({\delta }_1-{\delta }_2)F_{ab}$	$I_1-I_2+\left(1-t\right)\left(R_1-R_2\right)+\left(1-\lambda \right)F_{bc}+(1-\lambda ) {\delta }_1{F}_{ac}$
$E_8\left(1,1,1\right)$	${-\lambda \delta }_1\left(F_{ab}+F_{ac}\right)+C_a$	$-\lambda F_{bc}+C_b+\beta \left(I_1-I_2\right)+\lambda ({\delta }_1-{\delta }_2)F_{ab}$	$-I_1-I_2-\left(1-t\right)\left(R_1-R_2\right)-\left(1-\lambda \right)F_{bc}-(1-\lambda ) {\delta }_1{F}_{ac}$

.

According to the stability requirements of equilibrium points in evolutionary game theory, we analyze the stability of $E_8\left(1,1,1\right)$ in the Jacobian matrix to obtain the strategic conditions for central government environmental supervision, local government regulation, and pollution prevention green investment by polluting enterprises. When ${\lambda \delta }_2\left(F_{ab}+F_{ac}\right)>C_a$ and $-\lambda F_{bc}+C_b+\beta \left(I_1-I_2\right)+\lambda ({\delta }_1-{\delta }_2)F_{ab}<0$, the equilibrium point $E_8\left(1,1,1\right)$is in a stable state. In this situation, if the enterprise has excessive pollution emissions, the central government will impose heavier penalties on local governments and polluters, with penalties greater than the central government’s inspection costs. The punishment imposed by local governments on enterprises will be greater than the cost of supervision by local governments and the transfer of benefits from enterprises to local governments.

5. System Simulation

5.1. Benchmark Simulation

The parameters that need to be assigned to the model in this article are $R_1$, $R_2$, $I_1$, $I_2$, $C_a$, $C_b$, $F_{ab}$, $F_{ac}$, $F_{bc}$, $t$, $\beta$, ${\delta }_1$, ${\delta }_2$, $\lambda$. The specific parameter assignment and principles are shown in

Table 4. Parameter Values.

Parameters	Value	Selection Principle
$I_1$	10	According to the CSMAR database, the ratio of preventive green investments to remedial green investments is about 2:5.
$I_2$	4
$R_1$	10	In the equilibrium state, the income of polluting enterprises is equal to the expenditure. Therefore, $R_1=I_1$, $R_2=I_2$.
$R_2$	4
$F_{ab}$	10	According to the website of China’s Ministry of Environmental Protection, the ratio of penalties imposed by environmental inspectors on local governments to those imposed on polluters is about 5:4. After being interviewed, local governments will increase penalties on companies.
$F_{ac}$	8
$F_{bc}$	12
$C_a$	1	According to China’s Bureau of Statistics, the cost of environmental supervision for the central government is no less than CNY 303 million, and the cost of supervision for local governments is about three times that.
$C_b$	3
$t$	0.2	This assumes a basic corporate tax rate of 20 per cent.
$\delta$1	0.8	There are accidental factors that make it impossible for local governments to identify the pollution behavior of enterprises.
${\delta }_2$	0.5
$\beta$	0.2	This supposes the tax share for local governments is 0.2.
$\lambda$	0.2	This supposes that the probability of failure of the enterprise’s investment is 0.2.

. Specifically, $I_1$ represents the expenditure of the enterprise on expected green investment, while $I_2$ represents the expenditure of the enterprise on governance green investment. Considering the different characteristics of the two types of green investment, the expenditure on expected green investment is higher than that on governance green investment, with $I_1=10$ and $I_2=2. R_1$ represents the return of the enterprise on expected green investment, while $R_2$ represents the return on governance green investment. Without considering the investment risks, in the long run, the return on expected green investment is greater than that on governance green investment, because the former can improve clean production capacity, increase total factor productivity, save costs to a certain extent, and green products have a competitive advantage. Assuming an equilibrium state, the return on polluting enterprises is greater. Equivalent to expenditure, therefore, are $R_1=10, R_2=4. C_a$ and $C_{b }$are the costs of central government supervision and local government supervision, respectively. Generally speaking, local governments need to supervise a wider range of areas, so the cost of supervision is higher. Let $C_a=1$ and $C_b=3$. In addition, the punishment imposed by local governments on enterprises is greater than that imposed by the central government on local governments, that is ${F_{ab}<F}_{bc}$. For the central government, the purpose of inspection is more to urge local governments to take action and create a deterrent for them. Therefore, the punishment imposed by the central government on local governments is greater than that imposed on polluting enterprises, that is $F_{ab}>F_{ac}$. $F_{ab}=10, F_{ac}=8$, and $F_{bc}=12$, and the other parameter values are tax ratio, $t=0.2$. The ratio of information rent sharing between polluting enterprises and local governments is $\beta =0.2$. The probability of failure of the expected green investment by enterprises is $\lambda =0.2$. When local governments supervise, the probability of the central government discovering excessive pollution behavior by enterprises is ${\delta }_1=0.8$. When local governments do not supervise, the probability of the central government discovering excessive pollution behavior by enterprises is ${\delta }_2=0.5$.

Based on the above parameter settings, the stability results of the system evolution in the initial scenario are shown in

Table 5. Stability Results.

Equilibrium	${\mathit{E}}_1\left(0,0,0\right)$	${\mathit{E}}_2\left(0,0,1\right)$	${\mathit{E}}_3\left(0,1,0\right)$	${\mathit{E}}_4\left(1,0,0\right)$	${\mathit{E}}_5\left(0,1,1\right)$	${\mathit{E}}_6\left(1,0,1\right)$	${\mathit{E}}_7\left(1,1,0\right)$	${\mathit{E}}_8\left(1,1,1\right)$
$n_1$	+	+	+	-	+	-	-	-
$n_2$	+	-	-	+	+	-	-	+
$n_3$	+	-	+	+	-	-	+	-
Result	Instability point	Saddle point	Saddle point	Saddle point	Saddle point	Stable point	Saddle point	Saddle point

.

According to Table 5, $E_6\left(1,0,1\right)$ is the stable point of the system, and the simulation evolution trend of the system is shown in Figure 2. At this point, the selection of preventive green investment by polluting enterprises by the central environmental inspection team is effective, but the incentive for local governments to choose regulatory strategies is ineffective. This is consistent with the views of Xia et al. [29], that is, facing the pressure of higher-level inspections from the central government, local governments have strong and weak differences in regulatory responses, thereby reducing the institutional effectiveness of central environmental inspections. On the one hand, this affirms the effectiveness of the central environmental inspection team in motivating enterprises to carry out preventive green investment. On the other hand, local governments have chosen a non-regulatory strategy, indicating that they have not yet fully assumed their main responsibilities under the decentralized governance system. In order to fully leverage the institutional effectiveness of central environmental supervision, this article will change the assumptions and numerical simulations in the initial scenario to obtain policy tools and effective conditions to incentivize local governments to carry out supervision.

5.2. The Impact of Changes in Strategy Probability

Based on the above benchmark scenario, we will now change the initial strategy probability of the central government and local government and observe the strategic response of the green investment of polluting enterprises, so as to infer the impact of the central government’s environmental supervision on the green investment strategy of enterprises. Part (1) changes the initial strategy probability of local government and the strategy probability of the enterprise; part (2) changes the initial strategy probability of the central government and the strategy probability of the enterprise; part (3) is the change of the initial strategy probability of the central government and the strategy probability of the local government.

(1)

Probability changes in local government and corporate strategies.

Other parameters remain unchanged, and four different probability scenarios are set: (a) $\mathrm{y}=0.9$,$\mathrm{z}=0.5$; (b) $\mathrm{y}=0.1$,$\mathrm{z}=0.5$; (c) $\mathrm{y}=0.5$,$\mathrm{z}=0.9$; (d) $\mathrm{y}=0.5$,$\mathrm{z}=0.1$. The simulation results of the impact of initial probability changes on the evolution path of the central government are shown in Figure 3.

According to Figure 3, comparing subfigures (a) and (b), if the initial probability of preventive green investment by polluting enterprises remains unchanged and the initial probability of local government regulation decreases, there is no significant change in the speed at which central enterprises adopt inspection strategies to reach a stable point. Comparing subfigures (c) and (d), if the initial probability of local government regulation remains constant and the initial probability of pollution prevention green investment by polluting enterprises is smaller, then the speed at which central policies adopt inspection strategies to reach a stable point will be faster. This reflects that the current central environmental inspection policy mainly regulates the green investment behavior of enterprises, while the inaction of local governments has not been accurately identified, and targeted institutional design and reasonable arrangements should not be made.

(2)

Probability changes in central government and corporate strategies.

Similarly, keeping all other parameters constant, four different probability scenarios are set: (a) $\mathrm{x}=0.9$,$\mathrm{z}=0.5$; (b) $\mathrm{x}=0.1$,$\mathrm{z}=0.5$; (c) $\mathrm{x}=0.9$,$\mathrm{z}=0.9$; (d) $\mathrm{x}=0.5$,$\mathrm{z}=0.1$. The simulation results of the impact of initial probability changes on the evolution path of the central government are shown in Figure 4.

According to Figure 4, comparing subfigures (a) and (b), if the initial probability of preventive green investment by polluting enterprises remains unchanged, the initial probability of central government supervision decreases, and the speed at which local government strategies reach a stable point does not show significant changes. This further reflects that the current central environmental inspection and supervision government has not yet formed a deterrent effect on the strategic behavior of local governments. Comparing subfigures (c) and (d), if the initial probability of the central government inspection remains constant and the initial probability of pollution prevention green investment by polluting enterprises is smaller, then the speed at which central policies adopt inspection strategies to reach a stable point will be slower. This reflects the current situation where local governments have a relatively low willingness to invest in pollution prevention green projects for polluting enterprises. There are hospitals that they want to regulate, but their strategies are gradually shifting towards unregulated stability. The possible reason is that local governments choose to collude with enterprises.

(3)

Probability changes of central and local governments.

Similarly, keeping all other parameters constant, four different probability scenarios are set: (a) $\mathrm{x}=0.9$, y $=0.5$; (b) $\mathrm{x}=0.1$, $\mathrm{y}=0.5$; (c) $\mathrm{x}=0.9$, $\mathrm{y}=0.9$; (d) $\mathrm{x}=0.5$, $\mathrm{y}=0.1$. The simulation results of the impact of initial probability changes on the evolution path of the central government are shown in Figure 5.

According to Figure 5, comparing subfigures (a) and (b), if the initial probability of local governments remains constant, the higher the initial probability of central government supervision, the faster the speed at which pollution prevention green investment by polluting enterprises reaches a stable point. Comparing subfigures (c) and (d), if the initial probability of central government supervision remains constant and local governments choose a larger regulatory strategy, the speed at which pollution prevention green investment by polluting enterprises reaches a stable point will be faster. This reflects that both central government supervision and local government regulation currently have a promoting effect on preventive green investment by enterprises, and in comparison, the promoting effect of local government regulation is greater.

5.3. Impact of Changes in Policy Tools

Local governments and enterprises are the main responsible parties for air pollution control. The institutional design goals of the central government are to fully mobilize the initiative and enthusiasm of local governments and polluting enterprises; help them break through inherent thinking, technology, and talent bottlenecks; and form sustainable development capabilities. The purpose of central environmental supervision is to transmit environmental pressure through the joint supervision of the party and the government, promote local governments to fulfill their regulatory responsibilities, improve regulatory efficiency, and encourage polluting enterprises to actively fulfill their social responsibilities. They should make green investments in the use of clean energy, innovative clean production processes, and innovative green technologies; reduce pollution emissions; and improve energy utilization efficiency to achieve green transformation and the upgrading of enterprises from the root. Therefore, as shown in Table 5, ${\mathrm{E}}_8\left(1,1,1\right)$ is the system saddle point of the game between the central government, local governments, and polluting enterprises. To become a stable point in the system, ${\mathrm{E}}_8\left(1,1,1\right)$ must satisfy three negative eigenvalues. To achieve this strategic combination, further investigation is needed into the institutional details related to central environmental supervision, such as the penalties for non-compliance, inspection costs, and risks of green investment for enterprises. Next, this article will adjust the corresponding parameter settings and analyze the impact of changes in government tools and other institutional details on the effectiveness of central environmental inspection.

(1)

The severity of penalties imposed on local governments.

We change the magnitude of the central government’s punishment on local governments. The initial scenario is set to ${\mathrm{F}}_{\mathrm{a}\mathrm{b}}=10$, with a step size of 10, resulting in ${\mathrm{F}}_{\mathrm{a}\mathrm{b}}=15$ and ${\mathrm{F}}_{\mathrm{a}\mathrm{b}}=20$. The remaining parameter values are consistent with the baseline scenario, and the system simulation evolution path is obtained, as shown in Figure 6.

According to Figure 6, when ${\mathrm{F}}_{\mathrm{a}\mathrm{b}}=20$, the asymptotic stable point of the three-dimensional dynamical system is reached at ${\mathrm{E}}_8\left(1,1,1\right)$. Compared with the stable equilibrium ${\mathrm{E}}_6\left(1,0,1\right)$ in the initial scenario, it can be seen that increasing the punishment intensity can make local governments shift from non-regulatory strategies to regulatory strategies, and the greater the punishment intensity, the better the incentive effect on polluting enterprises and local governments.

(2)

Enterprise green investment risk.

We change the risk coefficient $\mathsf{\lambda }$ of enterprise preventive green investment, based on the initial scenario $\mathsf{\lambda }=0.2$, with a step size of 0.3, taking $\mathsf{\lambda }=0.5,\mathsf{\lambda }=0.8$, and other parameter values consistent with the baseline scenario, to obtain the system simulation evolution path, as shown in Figure 7.

According to Figure 7, the higher the risk coefficient λ of enterprise preventive green investment, the smaller the willingness of enterprise preventive green investment. This is also consistent with the fact that enterprise preventive green investment has uncertainty due to various factors. When the risk of enterprise preventive green investment is higher and the uncertainty of expected returns is greater, the enterprise is less willing to carry out preventive green investment. The existing research indicates that the corporate preventive green investment risk is closely related to the stock of corporate green knowledge [30], corporate property rights heterogeneity [31], and corporate maturity and scale [32]. Therefore, when conducting environmental inspections and supervision, both central and local governments should pay attention to factors such as the reserve of corporate green knowledge and corporate maturity. Notably, the results in Figure 6 show that as the direction of corporate preventive green investment increases, the probability of local governments adopting regulatory strategies also increases, which will obviously affect the effectiveness of central environmental inspections. Therefore, the local government regulation of enterprises should pay more attention to the conditions of the enterprises themselves, focusing on both environmental subsidies and penalties to jointly incentivize corporate green transformation.

(3)

Central government inspection costs.

By changing the cost of conducting environmental inspections by the central government, based on the initial scenario of ${\mathrm{C}}_{\mathrm{a}}=1$, with a step size of 2, taking ${\mathrm{C}}_{\mathrm{a}}=3$ and ${\mathrm{C}}_{\mathrm{a}}=5$, and other parameter values consistent with the baseline scenario, the system simulation evolution path is obtained, as shown in Figure 8.

Based on Figure 8, the cost of inspections influences the central environmental inspection strategy. By comparing Figure 8a,b with the baseline scenario, it can be seen that as the inspection cost increases, the central government’s planning evolves into non-inspection. With the rise in inspection costs, it is evident that the strategies of local governments and polluting enterprises also struggle to evolve towards regulation and anticipated green investment. In other words, the central environmental inspection system needs to design a reasonable inspection cost.

6. Conclusions and Policy Implications

Based on the analysis and numerical simulation of the “central government-local government-polluting enterprise” evolutionary game model, this paper explores the impact of the central environmental inspection team’s green investment decisions on enterprises and depicts the influence and evolution path of strategies of various relevant stakeholders under different scenarios.

The study shows that the current central environmental inspection system can effectively incentivize polluting enterprises to adopt preventive green investments, but there is a possibility of failure in motivating local governments’ regulatory strategies. Increasing penalties for local governments will help achieve incentive effects on them. The greater the risk of enterprises’ preventive green investments, the less the central government’s promotion of such investments. The cost of environmental inspections affects the effectiveness of the inspection system, and if the cost is too high, local governments and polluting enterprises will choose non-regulatory and end-type green investment strategic behaviors.

Based on these conclusions, this paper proposes the following policy recommendations:

(1)

Combine rewards and punishments and develop effective environmental policy tools. Strengthen penalties for local government supervision failures to enhance the effectiveness of central environmental inspections. Refine multi-measure inspection procedures. Design support mechanisms for central inspections to alleviate local economic pressures from air pollution control, such as establishing an environmental investment and financing system, providing talent training and technological transformation support, and offering financial and tax incentives to emission reduction enterprises. Incorporate air pollution control assessments into local government performance evaluations, clarify their significance in local official evaluations, increase the weight of these assessments, refine their content, and specify rewards and punishments.

(2)

Provide green investment subsidies. Consider the green knowledge and maturity of enterprises during supervision. Increase innovation subsidies for small enterprises with low green technology reserves, including direct financial support, tax incentives, and low-interest loans for preventive green investments, to enhance enterprise understanding, green technology development, and management, and to reduce investment risks.

(3)

Cut inspection costs and promote inspection system normalization. Strengthen accountability mechanisms in central environmental inspections, mobilize local government enthusiasm, enhance grassroots environmental awareness, and reduce costs. Achieve institutionalized regular operations, refine procedures, implement categorized and differential management, and avoid responsibility mismatches and “environmental accountability” and “one-size-fits-all” issues. Promote the inspection of legal construction, incorporate the accountability mechanism into the legal framework, and establish a comprehensive long-term environmental protection inspection and rectification mechanism.

The paper also has some limitations. Due to the availability of data, the existing data on corporate green investment, especially the panel data on prospective green investment and end-management green investment, are insufficient to support the corresponding empirical research. In future research, we will attempt to gather data from multiple sources and conduct relevant empirical studies.