Can Carbon Trading Promote Low-Carbon Transformation of High Energy Consumption Enterprises?—The Case of China

Abstract

This paper explores the effect of carbon trading on low-carbon transformation of high energy consumption enterprises in China. Based on the mechanism of interaction and restriction among high energy consumption enterprises, carbon verification agencies and the government, a tripartite evolutionary game model is constructed. The three-dimensional dynamic system is built to analyze the behavior patterns of the three parties. The evolution path of the tripartite game is visualized, and the low-carbon transformation states of high energy consumption enterprises in different situations are described. The results show that the high energy consumption enterprises, verification organization and the government cannot reach the optimal game equilibrium (low-carbon transformation, verification and supervision) temporarily when seeking their own interests. The corresponding measures should be taken with different situations of the tripartite game. No matter what strategy the government chooses, the low-carbon transformation could be promoted by carbon trading through carbon verification mechanism.

1. Introduction

With the global warming and deterioration of the resource environment [1], low-carbon transformation has become a general consensus [2]. The proposal of “double-carbon target” and the establishment of national carbon trading market [3] show the determination of China to cultivate new growth points in green [4] and low-carbon fields [5]. In this context, high energy consumption enterprises (hereinafter referred to as “enterprises”) as the main source of carbon emissions obviously cannot be immune [6]. Enterprises are the main consumption departments of fossil energy in China [7] and are also the main body of energy conservation, emission reduction and low-carbon transformation. However, due to high low-carbon cost and insufficient supply of clean energy, the motivation for low-carbon transformation in enterprises is insufficient [8]. The promotion of external forces is particularly important at this time.

Carbon trading is an effective market mechanism which plays an increasingly important role in low-carbon transformation [9,10]. Enterprises must strictly control carbon emissions according to the given carbon quota standards, otherwise they will have to bear the high fines of the government [11]. In this process, enterprises will naturally promote the development of low-carbon transformation by replacing traditional energy [12] and optimizing production processes [13]. As an intermediary force between enterprises and governments, whether the verification agency can reliably verify the carbon emissions of enterprises and truthfully report to relevant departments determines the effectiveness of low-carbon conversion work [14]. However, in consideration of maximizing their own interests, enterprises and verification agencies may collude [15]; thus, low-carbon transformation work is hindered. The government may also neglect supervision [16], which directly leads to the loss of endogenous motivation for low-carbon transformation. For the existence of the interaction mechanism among the government, the verification agency and the enterprise, game theory has become the best tool to study the behavior strategies of the three parties in the low-carbon transformation.

The existing research on low-carbon transformation mainly focuses on the exploration of development mode [17], the construction of indicator systems [18], the evaluation of the low-carbon transformation process and other aspects [19,20]. These studies are often based on the premise of fixed behavior mode of low-carbon actors, ignoring the impact of internal and external interaction mechanism on the low-carbon transformation process. Existing articles on the carbon trading market have conducted in-depth discussions on the impact of external factors such as carbon trading policies and economic indicators, but there is also a lack of interaction mechanisms between entities [21,22,23]. In fact, the government, enterprises and verification agencies are not static in the low-carbon conversion work. It is a process of long-term adjustment and dynamic change. Therefore, this paper uses the evolutionary game model with the characteristic of constant adjustment [24] to analyze the evolution process of tripartite behavior strategy. The dynamic picture of the tripartite game is described intuitively with evolutionary game theory [25]. Then, the low-carbon transformation path is optimized by adjusting the initial willingness and related parameters. This opens up a new perspective for the research of low-carbon transformation theory and also provides theoretical reference and practical basis for the development of low-carbon transformation work.

The remainder of this article is presented below. Section 2 introduces the model hypothesis and model construction. Section 3 finds the equilibrium point by constructing the Jacobian matrix of the three-dimensional dynamic system. The scenario analysis can be found in Section 4. Section 5 summarizes the relevant conclusions and enlightenments according to the research results.

2. Methodology

As an important subject of low-carbon transformation, carbon trading has a complex relationship of mutual influence and mutual restriction with enterprises and the government through carbon verification organization. Considering their own interests and China’s actual conditions, the three parties have both the motivation to adopt positive strategies and the possibility of leaning towards negative strategies at any time, hindering the development of low-carbon transformation. The tripartite will play games for a long time in the process of low-carbon transformation and constantly adjust their behaviors to adapt to the other two sides [26]. The low-carbon transformation work will also be continuously promoted in this process. The research on the process of the three-parties game is helpful to clarify their behavior patterns, change their behavior strategies and optimize the path of low-carbon transformation. The low-carbon transformation work will also continue to advance in this process.

2.1. Model Assumptions

The tripartite of the game consists of enterprises, verification agencies and local governments. The tripartite members all accord with the reality characteristic of bounded rationality and will make their own behavior judgment according to limited knowledge and information. Because of the limited knowledge and information, the three parties will adjust their own strategies according to the feedback of the other parties’ behavior in the game process. Enterprises can choose “low-carbon transformation” strategy or “maintain the status quo” strategy. The verification organization has two strategies, “verification” and “non-verification”, for the carbon emissions of enterprises. Correspondingly, the government can also choose a “regulation” or “non-regulation” strategy in the low-carbon transformation.

Enterprises have two strategies: low-carbon transformation and maintaining the status quo. Low-carbon transformation will inevitably bring about a decrease in carbon emissions to meet the emission control targets set by the government. On the contrary, maintaining the status quo will not achieve the emission reduction targets. The comprehensive income brought by energy conservation and emission reduction of enterprises in low-carbon transformation is recorded as V₁. The comprehensive income under the condition of maintaining the status quo is recorded as V₂ (V₂ < V₁). The cost of low-carbon transformation of enterprises is recorded as C₂. When the enterprise reaches the emission reduction target under government supervision, the enterprise will be given emission reduction subsidy S. When the enterprise fails to reach the emission reduction target under government supervision, the enterprise will be fined F₁. Therefore, because the verification results of the verification agency determine whether the enterprise receives the punishment, when the enterprise chooses the status quo strategy, the enterprise will have the incentive to bribe the verification agency. The amount of bribery shall be recorded as B. The verification organization will not strictly verify it after accepting the bribe. However, under the supervision of the government, the bribery of enterprises will inevitably fail. The bribes received by the verification agencies from enterprises B will also be confiscated.

Verification agencies have two strategies: verification and non-verification. If the verification agency performs due diligence to verify the carbon emissions of the enterprise [27], the government will give the verification agency an economic reward or subsidy, which is recorded as W. The verification cost of the verification agency is recorded as C₃. If that verification agency does not verify the carbon emissions of the enterprise under government supervision, not only will the verification agency not receive the corresponding economic return, but it will also be punished by the government, which is recorded as F₂.

The government has two strategies: regulation and non-regulation. The government here is assumed to be a local government, regardless of the influence of the higher government. If the enterprises adopt low-carbon transformation measures and actively reduce emission, the economic [28] and social benefits brought to the government are recorded as U₁. If the enterprises maintain the status quo, it is recorded as U₂ (U₂ < U₁). As mentioned above, in the case of effective government supervision of enterprises and verification agencies, positive verification agencies and enterprises (W and S) will be rewarded in the form of subsidies, and the supervision cost will be recorded as C₁. Otherwise, the penalty is F₂ and F₁ respectively.

2.2. Game Model Construction

According to the above basic assumptions and parameter settings about the tripartite behavior, the payoff matrix of the three-party game can be deduced, as shown in

Table 1. Payoff Matrix of Tripartite Game under Government Regulation (z = 1).

		Verification Agency
		Verification (y)	No Verification (1 − y)
enterprise	low-carbon transformation (x)	$V_1-C_2+S$	$V_1-C_2+S$
		$W-C_3$	$-F_2$
		$U_1-C_1-S-W$	$U_1-C_1-S+F_2$
	maintain the status quo (1 − x)	$V_2-F_1$	$V_2-B-F_1$
		$W-C_3$	$-F_2$
		$U_2-C_1-W+F_1$	$U_2-C_1+F_1+F_2$

and

Table 2. The Payoff Matrix of Tripartite Game under the Condition of No Government Regulation (z = 0).

		Verification Agency
		Verification (y)	No Verification (1 − y)
enterprise	low-carbon transformation (x)	$V_1-C_2$	$V_1-C_2$
		$-C_3$	$0$
		$U_1$	$U_1$
	maintain the status quo (1 − x)	$V_2-F_1$	$V_2-B$
		$-C_3$	$B$
		$U_2$	$U_2$

. Among them, the probability of low-carbon transformation of enterprises is x, and the probability of maintaining the status quo is 1 − x. The probability of serious verification by the verification agency is y, and the probability of non-verification is 1 − y. The probability of government regulation is z, and the probability of non-regulation is 1 − z. Since the behavioral probabilities of three parties vary from 0 to 1, the range of values for x, y and z is [0, 1].

According to the payment matrix, in the case of three parties (low-carbon transformation, verification, supervision), the income of the emission control enterprise is $V_1-C_2+S$, representing the sum of carbon reduction benefits and subsidies obtained by enterprises minus the cost of carbon reduction; the income of the verification agency is $W-C_3$, representing the economic subsidies granted by the government minus the verification costs; the government’s revenue is $U_1-C_1-S-W$, representing the economic and social benefits of carbon reduction minus regulatory costs and subsidy costs. In other cases, the three parties will receive different benefits as their behavior changes.

As a dynamic equation group reflecting the change trend of participants, the replication dynamic equation strongly depicts the behavior track of the game subject. By using the replication dynamic equation, the game evolution process of the government, verification organization and enterprise can be analyzed:

$$\frac{d\theta \left(t\right)}{dt}=\theta \left(t\right)·\left[E_t\left(S\right)-\overline{E_t}\right]$$

(1)

where $d\theta \left(t\right)/dt$ is the proportional growth rate of the population at time t when players choose a strategy S. $E_t\left(S\right)$ is the proportion of the population that chooses this strategy S for the participating population. $E_t\left(S\right)$ is the expected profit of choosing this strategy. $\overline{E_t}$ is the average expected return of two different strategies.

Suppose that the expected return of enterprises adopting low-carbon transformation strategy is E₁₁. The expected return of maintaining the status quo is E₁₂. The average expected return is $\overline{E_1}$. The average expected return of enterprises is a weighted average of the expected return of two different strategies, similar to other two parties. The expected return of verification organization selecting verification strategy is E₂₁. The expected return of non-verification is E₂₂. The average expected return is $\overline{E_2}$. The expected return of government selecting regulatory strategy is E₃₁. The expected return of non-regulation is E₃₂. The average expected return is $\overline{E_3}$. According to the definition of replication dynamic equation, the replication dynamic equations of enterprises, verification agencies and governments can be obtained:

$$\{\begin{array}{c}F\left(x\right)=dx/dt=x\left(E_{11}-\overline{E_1}\right)\\ F\left(y\right)=dy/dt=y\left(E_{21}-\overline{E_2}\right)\\ F\left(z\right)=dz/dt=z\left(E_{31}-\overline{E_3}\right)\end{array}$$

(2)

According to the income matrix, the expected return of the enterprise and government choosing the strategy of “low-carbon transformation”, the expected return of the “status quo” strategy chosen by enterprises and governments and the average expected payoff from different strategies, respectively, are expressed as

$$\{\begin{array}{c}{E}_{11}=V_1-C_2+zS\hfill \\ E_{12}=\left(1-z\right)\left(V_2-B\right)+y\left(1-z\right)\left(B-F_1\right)\hfill \\ \overline{E_1}=x{E}_{11}+\left(1-x\right)E_{12}\hfill \end{array}$$

(3)

The expected benefits of the verification organization choosing verification strategy and non-verification strategy and the average expected payoff from different strategies, respectively, are expressed as

$$\{\begin{array}{c}{E}_{21}=W-C_3\hfill \\ E_{22}=-z{F}_2+\left(1-x\right)\left(1-z\right)B\hfill \\ \overline{E_2}=y{E}_{21}+\left(1-y\right)E_{22}\hfill \end{array}$$

(4)

The expected returns of the government’s choice of regulatory strategy and non-regulatory strategy and the average expected payoff from different strategies, respectively, are expressed as

$$\{\begin{array}{c}{E}_{31}=-y\left(W+F_2\right)-x\left(S+F_1\right)+\left(U_1-C_1+F_2+F_1\right)\hfill \\ E_{32}=U_2+x\left(U_1-U_2\right)\hfill \\ \overline{E_3}=z{E}_{31}+\left(1-z\right)E_{32}\hfill \end{array}$$

(5)

According to Malthusian’s equation [29], the growth rate (dx/dt) of the proportion of enterprises choosing “low-carbon transformation” strategy over time is directly proportional to the difference between the expected payoff of E₁₁ and the average expected payoff of $\overline{E_1}$. The same goes for governments and verification agencies. Substitute Equations (3)–(5) into Equation (2), respectively. Thus, the dynamic evolution of the probability of the tripartite behavior strategy with time can be obtained so as to form a three-dimensional dynamic force system:

$$\{\begin{array}{c}F\left(x\right)=x\left(1-x\right)\left[V_1-C_2+zS+\left(z-1\right)\left(V_2-B\right)+y\left(z-1\right)\left(B-F_1\right)\right]\hfill \\ F\left(y\right)=y\left(1-y\right)\left[W-C_3+z{F}_2+\left(x-1\right)\left(1-z\right)B\right]\hfill \\ F\left(z\right)=z\left(1-z\right)\left[-y\left(W+F_2\right)-x\left(S+F_1\right)+\left(F_2+F_1-C_1\right)\right]\hfill \end{array}$$

(6)

To find the evolutionary equilibrium of the game system, let

$$\{\begin{array}{c}F\left(x\right)=0\\ F\left(y\right)=0\\ F\left(z\right)=0\end{array}$$

(7)

Then, Equation (7) is satisfied in the case of $R=\left\{\left(x,y,z\right)\right|0\le x\le 1,0 \le y\le 1,0 \le z\le 1\}$ and has nine equilibrium points, $P_1\left(0,0,0\right)$, $P_2\left(0,0,1\right)$, $P_3\left(0,1,0\right)$, $P_4\left(0,1,1\right)$, $P_5\left(1,0,0\right)$, $P_6\left(1,0,1\right)$, $P_7\left(1,1,0\right)$, $P_8\left(1,1,1\right)$, $P_9\left(x_0,y_0,z_0\right)$, which are also in the solution domain R. These points are also solutions of the system (8):

$$\{\begin{array}{c}{V}_1-C_2+zS+\left(z-1\right)\left(V_2-B\right)+y\left(z-1\right)\left(B-F_1\right)=0\hfill \\ W-C_3+z{F}_2+\left(x-1\right)\left(1-z\right)B=0\hfill \\ -y\left(W+F_2\right)-x\left(S+F_1\right)+\left(F_2+F_1-C_1\right)=0\hfill \end{array}$$

(8)

However, since $P_9\left(x_0,y_0,z_0\right)$ is a non-strict Nash equilibrium and does not meet the stability standard of evolutionary game of multi-agent model, we only need to consider the equilibrium point P₁–P₈.

3. System Stability Analysis

According to Friedman [30], the stability of the equilibrium point of an evolutionary system can be obtained by analyzing the local stability of the Jacobian matrix. Therefore, the Jacobian matrix of the three-dimensional dynamic system can be used to judge the local stability of the equilibrium point of the game among the government, enterprises and verification institutions. The Jacobian matrix of the three-dimensional dynamical system (8) can be represented by $\mathrm{J}$ as follows:

$$\begin{array}{c}\mathrm{J}=\left[\begin{array}{ccc}\frac{dF\left(x\right)}{dx}& \frac{dF\left(x\right)}{dy}& \frac{dF\left(x\right)}{dz}\\ \frac{dF\left(y\right)}{dx}& \frac{dF\left(y\right)}{dy}& \frac{dF\left(y\right)}{dz}\\ \frac{dF\left(z\right)}{dx}& \frac{dF\left(z\right)}{dy}& \frac{dF\left(z\right)}{dz}\end{array}\right]=\\ \left[\begin{array}{ccc}\left(1-2x\right)\left[\begin{array}{l}{V}_1-C_2+zS+\left(z-1\right)\left(V_2-B\right)\\ +y\left(z-1\right)(B-F_1)\end{array}\right]& x\left(1-x\right)\left[\left(z-1\right)\left(B-F_1\right)\right]& x\left(1-x\right)[S+V_2-B+y(B-F_1\left)\right]\\ y\left(1-y\right)\left[\left(1-z\right)B\right]& (1-2y)\left[\begin{array}{c}W-C_3+z{F}_2+\\ \left(x-1\right)\left(1-z\right)B\end{array}\right]& y\left(1-y\right)[F_2+(1-x\left)B\right]\\ z\left(z-1\right)\left[\left(S+F_1\right)\right]& z\left(z-1\right)\left[\left(W+F_2\right)\right]& \left(1-2z\right)\left[\begin{array}{l}-y\left(W+F_2\right)-x\left(S+F_1\right)\\ +\left(F_2+F_1-C_1\right)\end{array}\right]\end{array}\right]\end{array}$$

(9)

Friedman’s method for determining the stability of system points out that if a point is to be an equilibrium point of the three-dimensional dynamic system, all the eigenvalues of the point in the Jacobian matrix must be nonpositive. Therefore, the stability of each equilibrium point can be analyzed by substituting each equilibrium point into the Jacobian matrix and calculating the eigenvalue at each equilibrium point.

According to the eigenvalue of the equilibrium point and the value of parameters, we can determine whether the equilibrium point is the evolutionarily stable point. The value of the characteristic value at $P_9\left(x_0,y_0,z_0\right)$ is relatively complicated, and according to the stability judgment method of Friedman, $P_9\left(x_0,y_0,z_0\right)$ always satisfies the determinant Det(J) < 0 and Tr(J) = 0. Therefore, $P_9\left(x_0,y_0,z_0\right)$ is the saddle point of the system and cannot be the evolutionary equilibrium point. Thus, this paper will not analyze it in detail. The eigenvalues and stability of equilibrium points $P_1$–$P_8$ are shown in

Table 3. Eigenvalues and Stability of Jacobian Matrices at Equilibrium Points.

Equilibrium Point	Eigenvalue	Stability
$P_1\left(0,0,0\right)$	${\delta }_1=V_1-C_2+B-V_2$	When $V_1-C_2$ < $V_2-B$, $W-C_3<B$, $F_2+F_1>C_1$, it is a stable point
	${\delta }_2=W-C_3-B$
	${\delta }_3=F_2+F_1-C_1$
$P_2\left(0,0,1\right)$	${\delta }_1=V_1-C_2+S$ > 0	unstable point
	${\delta }_2=W-C_3+F_2$
	${\delta }_3=-\left(F_2+F_1-C_1\right)$
$P_3\left(0,1,0\right)$	${\delta }_1=V_1-C_2+F_1-V_2$	unstable point
	${\delta }_2=-\left(W-C_3-B\right)$ > 0
	${\delta }_3=-W+F_1-C_1$
$P_4\left(0,1,1\right)$	${\delta }_1=V_1-C_2+S$ > 0	unstable point
	${\delta }_2=-\left(W-C_3+F_2\right)$
	${\delta }_3=W-F_1+C_1$
$P_5\left(1,0,0\right)$	${\delta }_1=-(V_1-C_2+B-V_2)$	unstable point
	${\delta }_2=W-C_3$ > 0
	${\delta }_3=F_2-S-C_1$
$P_6\left(1,0,1\right)$	${\delta }_1=-(V_1-C_2+S)$	unstable point
	${\delta }_2=W-C_3+F_2$
	${\delta }_3=-(F_2-S-C_1)$ > 0
$P_7\left(1,1,0\right)$	${\delta }_1=-(V_1-C_2+F_1-V_2)$	When $V_1-C_2>V_2-F_1$,$W>C_3$, it is a stable point
	${\delta }_2=-\left(W-C_3\right)$
	${\delta }_3=-W-S-C_1$
$P_8\left(1,1,1\right)$	${\delta }_1=-(V_1-C_2+S)$	unstable point
	${\delta }_2=-\left(W-C_3+F_2\right)$
	${\delta }_3=W+S+C_1$ > 0

.

Due to the fact that the stable points must satisfy the non-positive eigenvalues in the Jacobian matrix, except that $P_1\left(0,0,0\right)$ and $P_7\left(1,1,0\right)$ satisfy the stable conditions under certain conditions, the remaining equilibrium points cannot satisfy the conditions and are unstable points. Therefore, this paper focuses on the two typical scenarios when the evolutionary equilibrium is $P_1\left(0,0,0\right)$ and $P_7\left(1,1,0\right)$. $P_1\left(0,0,0\right)$ is the evolutionary equilibrium point of the system; at this time, the characteristic values ${\delta }_1$, ${\delta }_2$ and ${\delta }_3$ are all less than zero. The tripartite all adopt negative behavior strategies, and the low-carbon transformation work is in the most negative state. From ${\delta }_3=F_2+F_1-C_1$ < 0 it can be seen that the government’s regulatory cost is too high, exceeding the possible fine amount for verification agencies and enterprises. Therefore, the government will not take active regulatory measures for its own interests. From ${\delta }_1=V_1-C_2+B-V_2$ < 0, we obtain $V_1-C_2<V_2-B$. Enterprises can obtain more benefits by maintaining the status quo without government supervision. Enterprises will not actively transform to low-carbon but maintain the status quo. From ${\delta }_2=W-C_3-B$ < 0, we obtain $W-C_3<B$. In the case of no government supervision, the verification organization will have greater benefits by accepting bribes from enterprises instead of conducting carbon verification on enterprises. Therefore, the verification organization will also adopt negative strategies, and the tripartite spontaneously reach a strategic equilibrium (maintaining the status quo, no verification and no supervision).

According to Table 3, since for $P_8\left(1,1,1\right)$ the value of eigenvalue ${\delta }_3$ is always greater than zero, $P_8\left(1,1,1\right)$ is not possible to be the equilibrium point of system evolution. When $P_7\left(1,1,0\right)$ is the evolutionary equilibrium point, it is the case closest to the optimal state. Therefore, this paper focuses on the case that $P_7\left(1,1,0\right)$ is the evolutionary equilibrium point. When eigenvalues ${\delta }_1$, ${\delta }_2$ are less than zero and eigenvalue ${\delta }_3$ is greater than zero, $P_7\left(1,1,0\right)$ is the evolutionary equilibrium point of the system. From ${\delta }_3=-W-S-C_1<0$, it can be seen that the government will pay a large regulatory cost and subsidy cost when both the verification institution and the enterprise take active actions. At this time, the government has no incentive to take active regulatory measures and will inevitably choose the “no regulation” strategy. From ${\delta }_1=-(V_1-C_2+F_1-V_2)$ < 0, $V_1-C_2>V_2-F_1$ it can be obtained that enterprises can obtain more benefits by adopting low-carbon transformation strategy without government supervision. For profit consideration, enterprises will take energy-saving and emission-reduction measures to promote production to reduce carbonization. From ${\delta }_2=-\left(W-C_3\right)$ < 0, $W-C_3>0$ it can be obtained that the benefits of verification activities of verification institutions are higher than the expected costs, so they will actively adopt the behavior strategy of strict verification. The tripartite spontaneously reached a strategic balance (transformation, verification and non-supervision) (for convenience of description, the low-carbon transformation is briefly recorded as transformation below).

4. Scenario Analysis

In order to explore the effect of carbon trading on low-carbon transformation of high energy consumption enterprises in China, this paper visualizes the possible situations of the tripartite game. Through the adjustment of initial willingness and relevant parameters to adjust the existing situation, the low-carbon transformation path is explored and optimized. Because the tripartite game is a dynamic process that changes with time, it is therefore necessary to discretize the Equations (1) and (2) to describe the asymptotic stable operation track of evolutionary game [31,32]. If the time step is set as Δt, it can be obtained from the definition of derivative:

$$\{\begin{array}{c}\frac{dx\left(t\right)}{d_t}\approx \frac{x\left(t+\Delta t\right)-x\left(t\right)}{\Delta t}\\ \frac{dy\left(t\right)}{d_t}\approx \frac{y\left(t+\Delta t\right)-y\left(t\right)}{\Delta t}\\ \frac{dz\left(t\right)}{d_t}\approx \frac{z\left(t+\Delta t\right)-z\left(t\right)}{\Delta t}\end{array}$$

(10)

According to the above formula, set the step Δt to 0.1, and use Matlab7.0 software to simulate the evolution path of three-party game.

4.1. Tripartite Negative Strategies

As can be seen from the above analysis, if and only if the eigenvalues ${\delta }_1$, ${\delta }_2$ and ${\delta }_3$ are all less than zero, $P_1\left(0,0,0\right)$ is the evolutionary stable point of the system. In this case, the parameters $V_1-C_2+B-V_2<0$, $W-C_3-B<0$ and $F_2+F_1-C_1<0$ must be satisfied simultaneously. At this time, the equilibrium result of the tripartite game is (maintain the status quo, no verification, no supervision). For convenience of description, this case is named Case 1. Based on the behavior patterns of various parties during the low-carbon transformation process, this article assigns values to parameters with reference to the relevant parameter settings in carbon reduction-related research [33,34,35]. Suppose that the government’s supervision cost $C_1=40$, the enterprise’s low−carbon transformation cost $C_2=70$, the verification cost of the verification organization $C_3=20$, the comprehensive income brought by the enterprise′s low-carbon transformation strategy $V_1=120$, the income of maintaining the status quo $V_2=110$, the low-carbon subsidy given by the government to the enterprise $S=30$, the verification remuneration given by the government to the verification organization $W=40$, and the penalty charged by the government when the enterprise maintains the status quo $F_1=20$. When the verification agency does not take verification measures, the government collects a fine of $F_2=10$, and the amount of bribes paid by enterprises to the verification agency $B=50$. The above parameters are not set in units but are only used to measure the relative size of each parameter. Assume that the initial willingness to act of the three parties is neutral (neither positive nor negative), and the initial behavior probability is 0.5. According to the three-dimensional dynamic system and its parameters, the three-dimensional dynamic evolution path of the behaviors of enterprises, verification agencies and governments can be described, as shown in Figure 1.

Figure 1 visually shows the evolution path of the behavior of the enterprise, the verification organization and the government over time in Case 1. When the initial intentions are medium (x = 0.5, y = 0.5, z = 0.5), it can be found that the three-dimensional curve quickly approaches from the starting point of (x = 0.5, y = 0.5, z = 0.5) to the equilibrium point of (x = 0, y = 0, z = 0). The tripartite finally reach a strategic equilibrium (maintain the status quo, no verification, no supervision). In this case, the cost of carbon reduction by enterprises is greater than government’s fines; the income of verification organizations after deducting verification cost is less than the amount of bribery by enterprises; and the government’s regulatory costs are greater than the total amount of fines imposed on enterprises and verification organizations. At this point, all three parties will choose negative strategies based on their own interests. At this time, the low-carbon transformation work is difficult to continue and is in the most negative state, so corresponding measures need to be taken to optimize the low-carbon transformation path. Next, this paper will discuss how to optimize the path of low-carbon transformation according to the specific process of the tripartite game.

Figure 2 depicts a two-dimensional evolutionary path of corporate, verification agency, and government behavior. Through the detailed description of the tripartite game behavior, we can further investigate the specific game process of the tripartite in the low-carbon transformation work. The horizontal axis represents time t, which has no specific meaning and is only used to investigate the convergence rate of the tripartite behavior strategy. The vertical axis represents the behavior probability of the three parties. The red, green and blue rays represent the changes of the behavior probability of the government, the verification organization and the enterprise, respectively. Since it is assumed that the initial willingness to act of the tripartite is neutral, the initial willingness probability of the three parties is set to 0.5. Thus, the three rays start from 0.5 at the same time.

From Figure 2, it can be found that the behavior probability of the three parties will eventually converge to 0. The difference lies in the speed of convergence. The audit institution converges to 0 faster than the enterprise, as shown in the figure. The green ray converges to 0 in a time t of 0.4, while the blue ray converges in a time t of 0.65. Because the government imposes a larger fine $F_1$ on firms than it imposes on the inspectors $F_2$, enterprises in the possible existence of government regulatory pressure will therefore delay the choice of “status quo” strategy. In addition, it can be found that the probability of behavior of verification agencies and enterprises will rise briefly and then decrease, obviously in response to possible government regulation. Over time, it can be found that the government has no regulatory willingness, and they will quickly adjust their probability of behavior to 0.

In case 1, for their own interests, the behavior strategies of the tripartite will eventually tend to be negative. Therefore, we try to adjust the relevant parameters to optimize the dynamic path of tripartite behavior evolution.

Keeping other parameters unchanged, reduce the cost of low-carbon transformation of enterprises C₂ to 65. Redraw the dynamic evolution path of the three-way game, as shown in Figure 3. Compared with Figure 2, it can be found that although the behavior probability of the tripartite will eventually tend to 0, the negative behavior of verification agencies and enterprises, however, has improved to a certain extent. In the figure, the green ray representing the behavior of the verification organization converges to 0 at a time t of 0.48. The blue ray representing the behavior of the enterprise converges to 0 at a time t of 1. Whether it is the verification organization or the enterprise, the convergence speed of the behavior probability to 0 has been restrained to some extent. The pace of corporate consolidation has slowed relatively more.

Obviously, reducing the cost of low-carbon transformation of enterprises is conducive to the improvement of the behavior of the tripartite game. Although it cannot change the final outcome of the game, it can delay the process of negative strategies adopted by the verification organization and enterprises. For enterprises, the reduction of low-carbon cost will make them more inclined to choose low-carbon transformation strategy. Under the possible regulatory pressure of the government, they will take low-carbon transformation measures for a period of time [36] and then turn to negative strategy. For the verification agency, the revenue situation has not changed. But due to the initial low-carbon transformation strategy of the enterprise, if it is not strictly checked under the supervision of the government, it will not only be unable to accept bribes from the enterprise but also be fined by the government. Therefore, the verification organization will also adjust its own behavior to a certain extent and slow down the speed of behavior probability tending to 0.

Through the adjustment of the cost of low-carbon transformation, the behavior strategy of the enterprise has been improved to a great extent. Next, the corresponding parameters of the verification organization are adjusted to observe whether the path of the tripartite game can be improved.

Fixing other parameters, the verification reward given by the government to the verification organization W is increased to 60. Redraw the dynamic evolution path of the tripartite game, as shown in Figure 4. Compared with Figure 1, it can be found that although the behavior of verification agencies has been greatly improved, the behavior of enterprises has not improved but deteriorated. The green ray representing the behavior of the verification agency converges to 0 at a time t of 0.86, rises sharply, and then falls in the short term. The blue ray representing the firm’s behavior converges to zero at a time t of 0.3. Obviously, the behavior probability of enterprises converges to 0 faster. The probability of action by the verification agency will not only slow down the speed of approaching 0 but will also increase significantly in the short term.

It can be concluded that the improvement of verification reward will enhance the work enthusiasm of verification organizations but will reduce the enthusiasm of enterprises for carbon reduction. The two diametrically opposed states of verification agencies and enterprises are not untraceable. Increasing the reward of the verification organization will certainly improve the verification enthusiasm of the verification organization. At least in the short term, the verification organization will be more inclined to choose the strict verification strategy. Generally speaking, enterprises should improve the probability of low-carbon transformation under the strict verification of verification agencies. However, enterprises choose to maintain the status quo strategy more quickly than before verification reward increases. This abnormal phenomenon is caused by the government’s non-supervision in the final analysis. Because the verification organization has high expectation of verification income, it will verify the low-carbon transformation status of enterprises and report to the government in order to obtain verification remuneration. However, due to the firm non-supervision behavior of the government, not only the verification organization cannot receive due remuneration, but the enterprise will also not be punished for maintaining the status quo. After receiving this information, the enterprise will speed up the adjustment of its own behavior, so the convergence speed of the behavior probability of the enterprise to 0 will be accelerated. The verification agency will also quickly adjust to the “no verification” strategy after identifying the government’s non-regulatory behavior. It is just that the convergence rate of the probability to 0 slows down for the inertia of the behavior.

4.2. Situations of Active Strategies

In the above, the situation that $P_1\left(0,0,0\right)$ is the stable point of system evolution is analyzed. Next, this paper will analyze the second situation, namely the situation that $P_7\left(1,1,0\right)$ is the stable point of system evolution. At this time, the equilibrium result of the tripartite game is (transformation, verification, no supervision). From the previous analysis, it can be seen that $P_7\left(1,1,0\right)$ is evolutionarily stable if and only if $-(V_1-C_2+F_1-V_2)<0$, $-\left(W-C_3\right)<0$ and $-W-S-C_1<0$. For convenience of description, this case is named Case 2. The relevant parameters are assigned based on the nature of the eigenvalues and the reality. Suppose $C_1=20$, $C_2=70$, $C_3=20$, $V_1=120$, $V_2=110$, $S=30$, $W=40$, $F_1=70$, $F_2=20$, $B=50$. In order to investigate the influence of different initial intentions on the behavior path, the initial intentions of the three parties are set to a lower state (x = 0.1, y = 0.1, z = 0.1). At this time, the three-dimensional dynamic evolution path of the tripartite game among enterprises, verification institutions and governments is redrawn, as shown in Figure 5.

Figure 5 visually shows the evolution path of the behavior of the enterprise, the verification organization and the government over time when the initial willingness is low (x = 0.1, y = 0.1, z = 0.1) in Scenario 2. It can be found that the three-dimensional curve quickly approaches from the starting point of (x = 0.1, y = 0.1, z = 0.1) to the equilibrium point of (x = 1, y = 1, z = 0). The tripartite finally reach the strategic equilibrium of (low-carbon transformation, verification and non-supervision). In this case, even if the government does not grant subsidies to enterprises, the carbon reduction benefits of enterprises are greater than maintaining the status quo. The revenue of verification organizations is greater than costs, and only the government lacks regulatory motivation due to high costs. Obviously, the low-carbon transformation work has been greatly improved at this time, and enterprises and carbon verification institutions are willing to take positive actions. However, the government still adopts negative strategies for its own interests. In the long run, it will dampen the enthusiasm of enterprises for low-carbon transformation. Therefore, this paper will discuss how to further optimize the path of low-carbon transformation according to the specific process of tripartite game.

Figure 6 depicts the game process of enterprises, verification agencies and governments in the low-carbon transformation work in Scenario 2. Similar to Figure 2, the red, green and blue rays represent changes in the probability of government, verification agency and enterprise behavior, respectively. In order to investigate the influence of initial intention on the outcome of the tripartite game, this paper sets the initial behavior probability of the three parties to 0.1. Compared with Case 1, we can find that the final result of the tripartite game in Case 2 has been improved to a greater extent. The verification organization and enterprises will spontaneously adopt positive behavior strategies to promote the development of low-carbon transformation. Although the government will eventually adopt the non-regulatory strategy, the probability of supervision will be increased at the initial stage and then gradually decreased. The blue and green rays representing the behavior probability of the enterprise and the verification organization will eventually converge to 1, and the convergence time t is 0.6. The red ray, which represents the probability of government action, rises rapidly to a peak over a period of time and then falls to zero.

Because the government will charge a relatively high fine for the negative behavior of the verification organization and enterprise (F₁ and F₂), whether the government regulates or not, verification agencies and enterprises will spontaneously choose the behavior strategies to promote the low-carbon transformation. Therefore, even if the government will finally choose not to supervise, the verification organization and enterprise will still firmly choose the positive behavior strategy. On the government side, as the verification agencies and enterprises are taking active measures, the government needs to pay more subsidies or remuneration to them. The government lacks the corresponding supervision motive force and will inevitably tend to passive supervision in the end. However, in the early stage of the game, the government is likely to take regulatory measures for a period of time, which aim to avoid the negative effects of possible negative strategies of verification agencies and enterprises on low-carbon transformation work. Once they are observed to be inclined to adopt an active strategy, the government deregulates them. This is the probability of the action rapidly approaching zero.

Since $W+S+C_1$ is always greater than zero, it is impossible to make $P_8\left(1,1,1\right)$ become the evolutionary equilibrium point of the system by adjusting the parameters. Therefore, this paper will further optimize Case 2 to make the tripartite game in the low-carbon transformation work reach a sub-optimal state.

Make other parameters unchanged, adjust the initial willingness of the government to 0.5 and 0.9, respectively. Redraw the dynamic evolution path of the tripartite game, as shown in Figure 7 and Figure 8. Comparing Figure 7 and Figure 8 with Figure 6, it can be found that the improvement of the government’s initial willingness not only strengthens the behavior probability of the government itself taking regulatory measures but also accelerates the convergence speed of the behavior probability of the verification organization and enterprise to 0. The convergence time t of the blue and green rays representing the behavior probability of the enterprise and the verification organization in Figure 7 is 0.45; the convergence time t of the blue and green rays in Figure 8 is 0.35. It shows that as the government’s initial willingness to regulate increases (0.1~0.9), the verification institutions and enterprises have also accelerated the pace of adjusting their own behavior probability to 1.

Obviously, the improvement of the government’s initial willingness is conducive to the improvement of the tripartite game path in the low-carbon transformation work. The improvement of the government’s initial willingness will strengthen the government’ s preference for regulatory strategy at first, although the government will eventually abandon the regulatory strategy in the interest of consideration. In the early game, however, the probability of the government’s action rises faster and approaches 1 when the initial willingness is high (z = 0.9). On the other hand, the higher initial willingness of the government will release a strong signal. The verification agency and enterprises will take corresponding measures quickly after observing the strong regulatory motivation of the government to avoid bearing the high fine from the government. At this time, the efficiency of low-carbon transformation work has been effectively improved, and the waste of resources in the process of tripartite strategy adjustment has been reduced.

Since improving the government’s initial regulatory willingness helps to improve the outcome of the tripartite game, we can try to increase the initial willingness of industry, verification agencies and governments at the same time. We also observe whether the simultaneous promotion of the three initial intentions can help to optimize the evolutionary path of low-carbon transformation.

Figure 9 depicts other parameters unchanged and the dynamic evolution path of the initial behavior of the enterprise, and the verification agency and the government is increased to 0.9 at the same time. Compared with Figure 6, Figure 7 and Figure 8, it can be found that the verification organization and enterprises further accelerate the convergence of the behavior probability to 1. As shown in the figure, the time t for the blue and green rays representing the behavior probability of enterprises and the verification organization to converge together is 0.12. By contrast, the government abandons regulation altogether and accelerates the rate at which the probability of action approaches 0. Instead of rising briefly, the red ray that represents the probability of a government’s action rapidly approaches 0 from the start.

The simultaneous ascension of all three initial intentions has not produced the desired results, and the three parties still have not reached an optimal balance (transformation, verification, supervision). While companies and verification agencies have stepped up the pace of adopting an active strategy, the government has become more passive than at the beginning. In the low-carbon transformation work, under the possible punishment pressure of the government, if the initial behavior probability is higher, the enterprises and verification agencies will certainly choose the positive behavior strategy more firmly. The government’s motivation is just the opposite because of the higher subsidies given to enterprises and verification agencies under government supervision. Once the other two sides are observed to be firmer in adopting active strategies, the government will quickly adjust to the non-supervision strategy. This would save on regulatory costs and reap the social benefits of a low-carbon transformation.

From Figure 6 to Figure 9, it can be found that when the tripartite game is in the sub-optimal equilibrium (transformation, verification and no supervision) in the low-carbon transformation work, the change of initial willingness is conducive to the improvement of the game situation. Increasing the government’s initial regulatory willingness not only accelerates the process of positive strategies adopted by verification agencies and enterprises but also improves the possibility of government adopting regulatory strategies to a certain extent. It should be noted that the simultaneous promotion of the initial willingness of the three parties has not completely improved the three-party game situation. While further strengthening the proactive strategy of verification agencies and enterprises, it also encourages the speculative mentality of the government. This is not conducive to the long-term development of low-carbon transformation [37].

5. Conclusions and Enlightenment

This paper discusses the effect of carbon trading on low-carbon transformation by a tripartite evolutionary game [38] model with the aid of the mechanism of mutual influence and restriction among enterprises, verification agencies and governments in low-carbon transformation. This model combines the evolutionary game theory to construct a three-dimensional dynamic system and analyzes the behavior patterns of the tripartite in the low-carbon transformation. Further, the evolution path of the tripartite behavior is analyzed in a scenario analysis. By adjusting the initial willingness and related parameters, this paper discusses the optimized path of low-carbon transformation.

The results show that the enterprise, the verification organization and the government cannot reach the optimal game equilibrium (transformation, verification, supervision) driven by their own interests. However, other situations that do not reach the optimal state can be optimized to improve the low-carbon transformation path. When the tripartite all adopt negative strategies, we can reduce the cost of low-carbon transformation and increase the reward of verification agency to strengthen the motivation of enterprises and verification agency to adopt positive strategy. Finally, sufficient policy space should be reserved for the government to reduce the environmental losses caused by both negative strategies. The low-carbon transformation of enterprises should not be carried out too hastily. Blind reducing coal use will lead to a sudden imbalance in the energy structure of enterprises. We should strengthen the support for low-carbon enterprises in tax preference, financing and project approval so as to effectively reduce the cost of low-carbon transformation of enterprises. Appropriate incentives should be given to verification agencies to calculate their verification costs in detail. The government should increase the punishment for its negative verification behavior and strengthen its willingness to verify.

When enterprises and verification agencies take active strategies and the government takes passive supervision, the key is to improve the initial supervision willingness of the government. The improvement of the government’s initial regulatory willingness not only effectively strengthens its own preference for regulatory strategies but also promotes enterprises and verification agencies to approach positive behavior strategies more quickly. It is worth noting that the policy effect of simultaneous improvement of the initial willingness of the tripartite is not ideal. Further strengthening the incentives for companies and verification agencies to adopt proactive strategies also encourages government speculation. Therefore, this will have a negative effect on the development of low-carbon transformation. The government’s negative regulatory willingness is mainly due to the higher regulatory costs. The government should speed up the liberalization of authority, optimize the administrative process and reduce the cost of multi-level administration. The government should also strengthen the training of regulators, improve regulatory efficiency and reduce labor costs. The findings suggest that carbon trading can greatly promote low-carbon transformation.

This paper breaks through the assumption that the behavior patterns of actors in research related to low-carbon transformation are fixed and introduces a tripartite evolutionary game model into low-carbon transformation research. Then, this paper puts forward corresponding policy suggestions for different situations and discusses how to improve the tripartite behavior strategy and optimize the low-carbon transformation path. This article has revealed the impact of internal and external interaction mechanisms on carbon reduction, and the conclusions drawn have implications for the behavioral research of governments, enterprises and verification organizations in the carbon trading market. They also provide theoretical reference and experimental basis for the implementation of low-carbon transformation work. In fact, public willingness [39], carbon prices [40] and other factors in the low-carbon transformation cannot be ignored. The intervention of these factors will affect the behavior patterns of governments, enterprises and verification organizations in the game and ultimately affect the equilibrium results of the game. How to establish the perfect external mechanism and further optimize the low-carbon transformation path is the future research direction.