Quadripartite Evolutionary Game of Sustainable Development of Supply Chain Finance with Government Participation

Abstract

Under the background of carbon peaking and carbon neutrality, green supply chain finance (GSCF) points out the sustainable development direction of supply chain finance (SCF). In order to study the mutual influence of GSCF participants’ decision-making and the effectiveness of government promotion, this paper builds an evolutionary game (EG) model that consist of “governments, financial institutions (FIs), core enterprises (CEs) and small- and medium-sized enterprises (SMEs)”, discusses the stability of strategy selection, and uses MATLAB to conduct numerical simulations. The research results show that: (1) Government’s participation can effectively promote the sustainable development of SCF; (2) In order to maximize incentives for FIs to carry out a GSCF business, large penalties for non-loan and subsidies similar to the income difference between traditional commercial loans and green loans (GL) should be implemented at the same time; (3) The stability of supply chain (SC) cooperation and reasonable risk compensation to CEs can promote its guarantee; (4) The increase in the expected profit of SC and the increase in the positive effect of GM in the industry are conducive to promoting GM in SMEs.

1. Introduction

With the change of market competition environment, the management mode of enterprises has changed from adopting technology and management upgrading to “horizontal integration” supply chain management (SCM) mode. However, most of the upstream partners are SMEs with financing constraints. Therefore, CEs begin to pay attention to SC financing. SCF guaranteed by CEs’ credit greatly alleviates the financing difficulties of upstream SMEs [1,2], promoting the development of SMEs. However, the rapid development of SMEs has also led to serious environmental pollution. With the introduction of environmental protection laws and policies, enterprises that cause environmental damage due to production will be subjected to strict compensation [3,4]. Large compensation payments make it difficult for SMEs to cover bank loans, and banks are reluctant to provide loans to SMEs for the consideration of capital security, so SC financing meets a bottleneck [5]. In the context of carbon peaking and carbon neutrality, the transformation of the SC industry is driven by the consumer demand-side green preference; the carbon trading mechanism is also promoting the innovation of the SCF model, and the traditional SCF is affected by many parties [6]. In addition to SCF, which relies on the credit guarantee of CEs, to improve the competitiveness of the whole SC, it is also necessary to strengthen the SC’s focus on “green”. Therefore, the research motivation of this paper is to solve the environmental pollution caused by the development of SMEs under the existing SCF model, crack the development bottleneck of SCF, and promote its sustainable development.

From the proposal of the “double carbon” goal to the accelerated construction of the “1+N” policy system of carbon peak and carbon neutralization, the development of China’s green industry has accelerated. In the 2022 semi-annual report of ten joint-stock banks, the key concerns and application scenarios announced in the SCF performance include going deep into green industries to carry out SCF, reflecting the ecological trend of focusing on pollution reduction and carbon reduction. The implementation of GSCF points out the direction for the sustainable development of SCF. Referring to Zarandi et al.’s [7] ideals of finding and solving problems to promote the future sustainable development of mankind, timely finding the problems of SCF in solving the financing constraints of SMEs and implementing appropriate solutions to solve it can promote the sustainable development of SCF.

EG theory synthesizes classic game theory and basic ideas of biological evolution. It holds that participants with limited knowledge and rationality will not choose the best strategy at the beginning, but can achieve a stable strategy of dynamic evolution through continuous learning and adjustment [8,9]. Participants in the GSCF system include the government, FIs, CEs, and SMEs. They adjust their behavior in the system through repeated decisions to obtain greater benefits. The mutual influence of strategy choices among them is suitable for EG theory to study. Therefore, based on the perspective of sustainable development of SCF with government participation, this paper uses EG theory to construct an EG model of GSCF system for strategic stability analysis. In a word, the research purposes of this paper are:

First, construct a quadripartite EG model of a GSCF system composed of government, FIs, CEs, and SMEs.

Second, the stability of the player strategy selection of the game model is analyzed to verify the validity of the government’s participation in the sustainable development of SCF.

Third, using MATLAB to simulate the dynamic evolution process of strategy based on the EG replication dynamic system, explore the influence of main factors on strategy selection.

Fourth, according to the research results, put forward policy suggestions to promote the sustainable development of SCF.

The contribution of this paper is to design a reward and punishment mechanism with government participation, and construct a quadripartite EG model of a GSCF system composed of government departments, FIs, CEs, and SMEs. It also discusses the conditions to be met when the strategy selection of participants reaches equilibrium, the effectiveness of government participation in the sustainable development of SCF, and the influence of the change of main factors on the strategy selection of participants.

The rest of this paper is organized as follows. In Section 2, the relevant literature is reviewed. Section 3 constructs the quadripartite EG model. The stability strategy choice of each participant is analyzed in Section 4. Section 5 analyzes the stability of the strategy combination. In Section 6, numerical simulations are carried out on the basis of theoretical analysis, and Section 7 gives the conclusion.

2. Literature Review

2.1. EG

Game theory was first proposed by Neumann et al. [10], and then Nash [11] proved the existence of Nash equilibrium, thus promoting the development of game theory. When game theory was widely used to study economic problems, biologists were inspired to try to construct various models of biological competitive evolution [12]. Then, biologists refined the Nash equilibrium of traditional game theory into an evolutionarily stable equilibrium and introduced selection mechanisms to construct a replicator dynamic model [13], since then, the traditional game theory was reformed and EG was formally formed. Subsequently, economists borrowed ideas from biologists and used EG to study economic problems [14,15], and promoted the development of EG. Based on bounded rationality, EG emphasizes the dynamic evolution process of game. As replicator dynamics are nonlinear, it is extremely difficult to find a unique solution, so EG is transformed from solving equilibrium to analyzing the stability of equilibrium, with evolutionary stable strategies (ESS) as the core [13]. Delaram et al. [16,17] proposed using game theory and stable matching to study the cloud manufacturing common platform according to the role and authority of participants. Zohreh et al. [18] investigated the EG of loan and credit between banks and customers based on EG theory, and used ESS to represent the optimal solution of the game. Kim et al. [19] investigated the pure strategy choices of the government and building owners based on EG theory, and obtained the positive ESS of the game.

2.2. SCF

SCF is a kind of financing business carried out by financial institutions (FIs) in accordance with the real business situation and the credit status of CE that provide guarantees to solve the problem of capital constraints of SMEs [20]. Previous studies on SCF mostly focused on operation mode [21,22], risk assessment [23,24,25,26], empirical analysis on the alleviation of financing constraints of SMEs [27,28], and the game model among various players [29,30,31,32,33]. Nowadays, the bottleneck of SCF development caused by environmental pollution of SMEs has attracted much attention from scholars. For example, Song [34] and Li et al. [35] pointed out that previous studies on SCF focused on the optimization of SC capital flow, without considering social and environmental issues, and that the sustainable development of SCF under the background of double carbon should bear sustainable social responsibilities. Fan et al. [36] founded that green credit, as an important financial tool for enterprises to reduce emissions, can significantly reduce environmental pollution.

In a word, scholars have conducted a wealth of studies on the operation mode, risk assessment, the mitigation effect of financing constraints on SMEs, and the game problems in the process of mitigation of SCF, but there lacks consideration of the sustainable development of SCF. This paper focuses on the sustainable development direction of SCF and GSCF financing status. The method of EG is adopted to study.

2.3. GSCF

At present, the development of GSCF is still in its infancy in our country. The development of green finance in China is mainly promoted by the government’s administrative means and lacks sustainability [37]. Considering the inestimable benefits and risks of SMEs’ green innovation efforts, as well as their lack of sufficient assets as collateral and low credit rating, banks tend to give up providing GL for SMEs [38]. The relevant researches mainly focus on the theoretical cracking ideas and game frame of GSCF development.

In terms of solving this problem, a class of studies proposed that the guarantee based on CEs could smoothly promote the solution of this problem [5,39]. A group of studies proposed that government subsidies and protective financing could reduce environmental pressure on corporate economic activities [40,41]. Another kind of research also suggested that banks can develop policies to help SMEs obtain GL [42]. The French Innovation Agency Public Investment Bank, for example, provides preferential interest rates and unsecured loans to SMEs that adopt environmentally friendly technologies and develop new ones.

As for the game research framework, the research usually included the game between two and three players. In terms of two players, the game between SMEs and CEs showed that the optimization of guarantee behavior of CEs and the close cooperation between FIs and CEs can promote the development of GSCF business [5], and the low loan interest rate of banks and government subsidies played a crucial role in the development of GSCF business [43], therefore, green credit financing of banks has the effect of easing the financial pressure of suppliers and can enhance the enthusiasm of suppliers to reduce emissions [44]. In terms of three players, the game between FIs, CEs, and SMEs showed that the larger the expected income and default cost of SMEs, the less inclined they are to default, and the game system can evolve to an ideal stable state [31], and the intervention mechanism of government subsidies and penalties can help improve the speed of system evolution to an ideal stable state [32]. A systematical study of the quadripartite game between government departments, FIs, CEs, and SMEs is still lacking.

In summary, to promote the development of GSCF, scholars have conducted in-depth research theoretically and proposed corresponding methods. However, it has the following deficiencies: (1) Most studies are a two-party game between SMEs and CEs, and only introduce the FI’s loan as a parameter into the model. Though the theoretical model is simplified, it cannot fully reflect the real situation; (2) Some studies introduce the government intervention mechanism to extend the game framework to a three-party among SMEs, CEs, and FIs, which improves the integrity of the model. However, the development of GSCF relies heavily on fiscal and tax intervention, and it is difficult to reflect the complex process of business development without including government departments in the game framework. Therefore, this paper constructs a quadripartite EG model composed of government departments, FIs, CEs, and SMEs to study the GSCF system that promotes sustainable development of SCF, so as to reflect the real situation of business development in a more complete way, which is of great significance.

3. EG Method and Model Construction

3.1. EG Theory

The development of GSCF mainly involves local governments, FIs, SMEs, and CEs. Among them, SMEs with their own emission rights to pledge to FIs to initiate GL application, is the capital demand side; CEs guarantee GL for SMEs; FIs examine CEs or SMEs to decide whether to grant GL; local governments supervise the production practices of SMEs. The decision-making behavior of each subject is a dynamic and repeated process: (1) Whether SMEs carry out green production management will have an impact on their business dealings with FIs and cooperation between CEs in the later stage, as well as the punishment from local government supervision; (2) Whether the CEs is willing to give credit guarantee depends on the past performance of the SMEs and the benefits brought by the guarantee behavior; (3) Whether the FIs lend or not is related to whether the SMEs have the guarantee of the CEs, the credit status of the CEs and SMEs in the past and the government rewards that the loans can obtain; (4) Whether local governments choose to carry out strict supervision or not depends on the direct benefits obtained from strict supervision and the losses caused by environmental pollution. Therefore, each subject makes repeated choices based on the other’s strategy, so that the system reaches equilibrium. EG believes that the players are bounded rationality and choose strategies through some transfer mechanism, emphasizes the dynamic evolution process of game, and focuses on the stability analysis of equilibrium, which can be used as a reliable method to study the interaction and influence mechanism of participants in the sustainable development of SCF.

3.2. Game Players and Their Strategy Choices

3.2.1. Government

The strategy choice of government departments is (Strict supervision, Loose supervision). First of all, government departments strictly supervise the production behaviors of SMEs, and take measures such as limiting production, stopping production, and imposing fines on non-green production behaviors. Secondly, by implementing guarantee risk compensation for CEs, government departments encourage them to provide credit guarantee for the GSCF financing business of SMEs, thus increasing the probability of SMEs obtaining loans. Finally, the government acts on FIs through business compensation and punishment of GSCF business loans to encourage them to provide GL for SMEs with insufficient funds for GM.

3.2.2. FIs

The FI’s strategy choice is (Loan, No loan). SMEs often have limited funds, and they must pay extra costs to adopt GM, which seriously leads to the lack of green production power, so FIs have become the core decision of whether SMEs can carry out GM. If FIs provide GL, SMEs have enough funds for GM. On the contrary, SMEs have a lack of funds and are unable to carry it out.

3.2.3. CEs

CE’s strategy choice is (Guarantee, No guarantee). First of all, SMEs often cannot obtain financial support from FIs due to lack of credit, lack of collateral, and other reasons, while the credit guarantee from the leading CEs in the SC can make credit endorsement for SMEs, so that they can obtain it. Secondly, the CE’s guarantee is responsible for supervising the production behavior of SMEs. Due to information symmetry, the CEs must be able to discover the non-green production behavior of SMEs and stop it in time to avoid serious losses.

3.2.4. SMEs

SME’s strategy choice is (Adopt GM, Not adopt GM). SMEs have the independent choice of production management, but often due to capital constraints, it is not possible to improve it (such as purchasing energy-saving equipment, transforming existing technology, and paying attention to pollution prevention and control, etc.), and result in resource waste and environmental pollution. Emission rights are granted by the government through administrative means to the enterprise, which has the value attribute. SMEs with emission rights can evaluate it as collateral and apply to FIs for GSCF financing under the guarantee of the CEs in the SC to solve the problem of capital shortage.

3.3. Model Hypothesis and Parameter Description

In accordance with the ideas of machine learning feature selection in Soltanzadeh et al. [45], to reduce the impact of irrelevant factors on the model, this paper established an EG model based on the actual situations and the following assumptions based on existing research theories.

(1) The government departments, FIs, CEs, and SMEs of the game are all bounded rationality, aiming to maximize their own interests. SMEs adopt GM with the probability of $m$, and do not adopt GM with the probability of $1-m$. The government departments strictly supervise with probability $x$ and loosely supervise with probability $1-x$. The probability that FIs chooses to loan is $y$, the probability that it does not loan is $1-y$. The probability that CEs chooses guarantee is $z$, and the probability that it does not guarantee is $1-z$, $m,x,y,z\in [0,1]$.

(2) When CEs is guaranteed, SMEs can obtain the GL with scale $D_1$ and the corresponding interest rate is $r$. In this case, FIs will pay a certain audit cost to audit the CEs, which can be ignored compared with the cost of directly auditing the SMEs without the guarantee of the CEs. When CEs do not provide guarantee, if FIs loan to SMEs, they need to pay the cost $C_f$ to directly evaluate SMEs, and issue GL $D_2$ after passing the evaluation $(D_1>D_2)$ [31]. The interest rate for traditional commercial loan is $r_0$$(r<r_0)$, and the CE’s guarantee rate is $\sigma$.

(3) SMEs are the upstream suppliers of CEs, and their own capital is $D_0$. They need to pay extra green cost $W$ to adopt GM. SMEs which do not adopt GM with their own funds can obtain benefits $R_b$, and bring benefits $E_b$ to downstream CEs. SMEs get GL $D_1$ and adopting GM can get benefits $R_{g1}$, and not adopting GM can get benefits $\Delta R_b^{\prime }$. Meanwhile, it brings benefits $E_{g1}$ and new benefits $\Delta E_b^{\prime }$ to downstream CEs, respectively. SMEs get GL $D_2$ and adopting GM can obtain benefits $R_{g2}$, and not adopting GM can obtain new benefits $\Delta R_b^{″}$. Meanwhile, they bring the downstream CEs benefits $E_{g2}$ and $\Delta E_b^{″}$, respectively.

(4) When SMEs apply for GL, they need to pay emission right valuation fee $H$ [46]. GM can obtain positive industry effects $S_h$, such as increase in order quantity and increase in wholesale price, etc., while negative industry losses $F_m$, such as production restriction, production suspension, and customer resource loss, etc., can be suffered when GM is not adopted [47].

(5) When SMEs cannot repay the loan, the CEs will pay for it if it provides credit guarantee. The occurrence of guarantee makes the cooperation and supervision between the two parties closer. In order to avoid losses caused by SMEs not adopting GM, the supervision cost of guarantee of CEs is set as $C_c$ [48]. In the case of repayment on behalf of the CEs, SMEs are punished $F$, and the trust-breaking behavior leads to the loss of the SC’s future expected earnings $V_1$ [31]. SMEs bear reputational losses $V_2$ when they cannot repay the loan to FIs. When the CEs does not guarantee, due to information asymmetry, the government departments cannot timely detect the environmental pollution caused by SMEs not adopting GM. SMEs with their own funds will cause environmental losses $N_b$; $\Delta N_b^{\prime }$ and $\Delta N_b^{″}$ are the new environmental losses after obtaining GL $D_1$ and $D_2$. When the pollution is founded by government, SMEs will be punished, and this will result in the disruption of SC business and make loss $V_3$ for CEs.

(6) Local government department’s strict supervision behaviors can obtain policy benefits $U_g$ from the central government directly or indirectly [49]. The strict supervision cost is $C_g$, and business subsidies are provided to FIs implementing GSCF loans, with a subsidy coefficient of $\alpha$. FIs that fail to implement GSCF loans are punished, and the penalty coefficient is $\beta$ [50]. In order to promote the willingness of SMEs and CEs to cooperate, risk compensation is carried out for CEs implementing the guarantee strategy, and the compensation coefficient is $\lambda$ [32]. SMEs that do not adopt GM as agreed will be fined $T$.

The parameters are summarized as shown in

Table 1. The model variables and explanations.

Variable	Explanation
$r$	The interest rate of GL.
$r_0$	The interest rate of traditional commercial loan.
$D_0$	The own capital of SMEs.
$D_1$	The GL scale of FIs with the guarantee of CEs.
$D_2$	The GL scale of FIs without the guarantee of CEs.
$C_f$	The evaluation cost of FIs to evaluate SMEs without the guarantee of CEs.
$W$	The extra green cost SMEs need to pay to adopt GM.
$R_b$	The benefits of SMEs that do not adopt GM with their own funds.
$\Delta R_b^{\prime }$	The new benefits of SMEs that do not adopt GM with the loan scale of $D_1$.
$\Delta R_b^{″}$	The new benefits of SMEs that do not adopt GM with the loan scale of $D_2$.
$E_b$	The benefits of CEs when SMEs do not adopt GM with their own funds.
$\Delta E_b^{\prime }$	The new benefits of CEs when SMEs do not adopt GM with the loan scale of $D_1$.
$\Delta E_b^{″}$	The new benefits of CEs when SMEs do not adopt GM with the loan scale of $D_2$.
$R_{g1}$	The benefits of SMEs that adopt GM with the loan scale of $D_1$.
$R_{g2}$	The benefits of SMEs that adopt GM with the loan scale of $D_2$.
$E_{g1}$	The benefits of CEs when SMEs adopt GM with the loan scale of $D_1$.
$E_{g2}$	The benefits of CEs when SMEs adopt GM with the loan scale of $D_2$.
$H$	The emission right valuation fee of SMEs.
$S_h$	The positive industry effects of SMEs adopt GM.
$F_m$	The negative industry losses of SMEs do not adopt GM.
$C_c$	The supervision cost of guarantee of CEs.
$F$	The amount of penalty of SMEs when CEs repay the loans for it.
$V_1$	The future expected benefits SMEs will lose when CEs repay the loans for it.
$V_2$	The reputational losses of SMEs when they cannot repay the loan to FIs.
$N_b$	The environmental losses of government when SMEs do not adopt GM with their own funds.
$\Delta N_b^{\prime }$	The new environmental losses of government when SMEs do not adopt GM with the loan scale of $D_1$.
$\Delta N_b^{″}$	The new environmental losses of government when SMEs do not adopt GM with the loan scale of $D_2$.
$V_3$	The losses of SC disruption of CEs.
$U_g$	The policy benefits of government when it adopts strict supervision.
$C_g$	The strict supervision cost of government.
$\alpha$	The subsidy coefficient of FIs that provide green loans.
$\beta$	The penalty coefficient of FIs that do not provide green loans.
$\lambda$	The compensation coefficient of CEs that provide guarantee.
$T$	The fine of SMEs that do not adopt GM.
$x$	The probability of government choosing strict supervision.
$y$	The probability of FIs choosing loan.
$z$	The probability of CEs choosing guarantee.
$m$	The probability of SMEs choosing GM.

. The payoff matrix is shown in

Table 2. Payment matrix of GSCF quadripartite game.

				CEs
				Guarantee		No Guarantee
				SMEs		SMEs
				Adopt GM	Not Adopt GM	Adopt GM	Not Adopt GM
Government	Strict supervision	FIs	Loan	$U_g-C_g-[\alpha +\lambda (1+r)]D_1$ $(r+\alpha )D_1$ $E_{g1}+[\sigma +\lambda (1+r)]D_1-C_c$ $R_{g1}-W-[\sigma +(1+r)]D_1-H+S_h$	$U_g-C_g-[\alpha +\lambda (1+r)]D_1$ $(r+\alpha )D_1$ $[\sigma +(\lambda -1)(1+r)]D_1-C_c+F$ $-R_{g1}+W-F-V_1-\sigma D_1-H-F_m$	$U_g-C_g-\alpha D_2$ $(r+\alpha )D_2-C{}_f$ $E_{g2}$ $R_{g2}-W-(1+r)D_2-H+S_h$	$U_g-N_b-\Delta N_b^{\prime \prime }-C_g-\alpha D_2+T$ $(\alpha -r-1)D_2-C{}_f$ $E_b+\Delta E_b^{\prime \prime }-V_3$ $R_b+\Delta R_b^{\prime \prime }-T-H-V_2-F_m$
			No loan	$U_g+\beta D_1-C_g$ $(r_0-\beta )D_1$ $0$ $S_h-D_0$	$U_g+\beta D_1-C_g+T-N_b$ $(r_0-\beta )D_1$ $E_b$ $R_b-T-F_m$	$U_g+\beta D_2-C_g$ $(r_0-\beta )D_2$ $0$ $S_h-D_0$	$U_g+\beta D_2-C_g+T-N_b$ $(r_0-\beta )D_2$ $E_b-V_3$ $R_b-T-F_m$
	Loose supervision	FIs	Loan	$0$ $r{D}_1$ $\sigma D_1+E_{g1}-C_c$ $R_{g1}-W-[\sigma +(1+r)]D_1-H+S_h$	$0$ $r{D}_1$ $(\sigma -r-1)D_1-C_c+F$ $-R_{g1}+W-F-V_1-\sigma D_1-H-F_m$	$0$ $r{D}_2-C_f$ $E_{g2}$ $R_{g2}-W-(1+r)D_2-H+S_h$	$-N_b-\Delta N_b^{″}$ $r{D}_2-C_f$ $E_b+\Delta E_b^{″}$ $R_b+\Delta R_b^{″}-(1+r)D_2-H-F_m$
			No loan	$0$ $r_0{D}_1$ $0$ $S_h-D_0$	$-N_b$ $r_0{D}_1$ $E_b$ $R_b-F_m$	$0$ $r_0{D}_2$ $0$ $S_h-D_0$	$-N_b$ $r_0{D}_2$ $E_b$ $R_b-F_m$

Note: Each grid from top to bottom represents the benefits of government departments, FIs, CEs, and SMEs.

.

4. Replicator Dynamic Equation and Evolutionary Stable Strategy

4.1. Stable Strategy Analysis of Government

The expected benefits $U_{11}$ of strict supervision and $U_{12}$ of losses by government are:

$$\begin{array}{ll}{U}_{11}=& yzm{\Pi }_1+yz(1-m){\Pi }_5+y(1-z)m{\Pi }_9+y(1-z)(1-m){\Pi }_{13}+(1-y)zm{\Pi }_{17}+(1-y)z\\ & (1-m){\Pi }_{21}+(1-y)(1-z)m{\Pi }_{25}+(1-y)(1-z)(1-m){\Pi }_{29};\end{array}$$

(1)

$$\begin{array}{ll}{U}_{12}=& yzm{\Pi }_{33}+yz(1-m){\Pi }_{37}+y(1-z)m{\Pi }_{41}+y(1-z)(1-m){\Pi }_{45}+(1-y)zm{\Pi }_{49}+(1-y)\\ & z(1-m){\Pi }_{53}+(1-y)(1-z)m{\Pi }_{57}+(1-y)(1-z)(1-m){\Pi }_{61}.\end{array}$$

(2)

Therefore, the replicator dynamic equation is:

$$F(x)=dx/dt=x(1-x)({\mathrm{U}}_{11}-{\mathrm{U}}_{12})=x(1-x)A(y,z,m)$$

(3)

where $A(y,z,m)=\{C_g-U_g+(1-m)(yz-1)T-(1-z)[\beta (1-y)-\alpha y]D_2+z(\alpha y-\beta +\beta y+y\lambda +ry\lambda )D_1\}$.

Let $m_0=1+\frac{U_g-C_g+(1-z)[\beta (1-y)-\alpha y]D_2-z(\alpha y-\beta +\beta y+y\lambda +ry\lambda )D_1}{(1-yz)T}$, then

(1) when $m=m_0$, $F(x)\equiv 0$, so any $x\in [0,1]$ is a stable point;

(2) When $m\ne m_0$, according to $F(x)=0$, there are two zeros $x=0$ and $x=1$, namely, “loose supervision“ and “strict supervision” by government departments which are both stable strategies.

Theorem 1.

When$0<m<m_0$, the government’s stable strategy is strict supervision. When$m_0<m<1$, the government’s stable strategy is loose supervision.

For the proof of theorem 1, see Appendix A, “Proof of theorem 1”. Theorem 1 shows that the decline in the probability of SMEs choosing GM will change the government’s stable strategy from loose supervision to strict. Similarly, the increase of probability of SMEs choosing GM will change the government’s stable strategy from strict supervision to loose supervision. Therefore, if SMEs can earnestly fulfill their social responsibilities and take the initiative to adopt GM measures, instead of having a lucky mind to not carry out GM and cause environmental pollution, they can avoid punishment from the government and prevent unnecessary losses to themselves and the SC it is in.

Further, by calculating the first partial derivative of $m_0$ with respect to $C_g$ and $U_g$, $\partial m_0/\partial C_g=-1/(1-yz)T<0$, $\partial m_0/\partial U_g=1/(1-yz)T>0$ can be obtained, that is, $m_0$ is negatively correlated with $C_g$ and positively correlated with $U_g$. It shows that when the cost of strict supervision is greater, the government will not adopt strict supervision strategy. Therefore, SMEs tend not to adopt GM. When local government departments can obtain more policy benefits from the central government through strict supervision, they will adopt strict supervision strategies, and therefore, SMEs will carry out GM according to the agreement.

4.2. Stable Strategy Analysis of FIs

The expected benefits $U_{21}$ of loan and $U_{22}$ of not loan by FIs are:

$$\begin{array}{ll}{U}_{21}=& xzm{\Pi }_2+xz(1-m){\Pi }_6+x(1-z)m{\Pi }_{10}+x(1-z)(1-m){\Pi }_{14}+(1-x)zm{\Pi }_{34}+(1-x)\\ & z(1-m){\Pi }_{38}+(1-x)(1-z)m{\Pi }_{42}+(1-x)(1-z)(1-m){\Pi }_{46};\end{array}$$

(4)

$$\begin{array}{ll}{U}_{22}=& xzm{\Pi }_{18}+xz(1-m){\Pi }_{22}+x(1-z)m{\Pi }_{26}+x(1-z)(1-m){\Pi }_{30}+(1-x)zm{\Pi }_{50}+(1-x)\\ & z(1-m){\Pi }_{54}+(1-x)(1-z)m{\Pi }_{58}+(1-x)(1-z)(1-m){\Pi }_{62}.\end{array}$$

(5)

Therefore, the replicator dynamic equation of FIs is:

$$F(y)=dy/dt=y({\mathrm{U}}_{21}-{\mathrm{U}}_2)=y(1-y)({\mathrm{U}}_{21}-{\mathrm{U}}_{22})=y(1-y)B(x,z,m)$$

(6)

where $B(x,z,m)=y(1-y)\{[(z-1)(r_0-r+x(1-\alpha -\beta +2r))+mx(1+2r)(1-z)]D_2+$ $(z-1)C_f+z(r-r_0+\alpha x+\beta x)D_1\}$.

Let $m_0=\frac{C_f+[r_0-r+x(1-\alpha -\beta +2r)]D_2}{x(1+2r)D_2}-\frac{z[r-r_0+x(\alpha +\beta )]D_1}{x(1+2r)(1-z)D_2}$, then

(1) when $m=m_0$, $F(y)\equiv 0$, so any $y\in [0,1]$ is a stable point;

(2) When $m\ne m_0$, according to $F(y)=0$, there are two zeros $y=0$ and $y=1$, namely, “no loan” and “loan”.

Theorem 2.

When$0<m<m_0$, the stable strategy of FIs is not loan. When$m_0<m<1$, the stable strategy is loan.

For the proof of theorem 2, see Appendix A, “Proof of theorem 2”. Theorem 2 shows that the decline in the probability of SMEs adopting GM will change the stable strategy of FIs from loan to no loan. Similarly, the increase in the probability of SMEs adopting GM will change the stable strategy of FIs from no loan to loan. In the case that CEs do not provide guarantee, FIs need to pay costs to examine SMEs. In addition, SMEs that do not adopt GM and cause environmental pollution will suffer from punishment from strict supervision government departments, and the punished SMEs will let FIs suffer losses because they are unable to repay loans. However, in the case of CE’s guarantee, there is no need to pay the examination cost for FIs. Even if there is governmental strict supervision, FIs can obtain the loan repaid on behalf of the CEs, and with less loss. Considering the existence of loan risk, FIs will choose loan when SMEs adopt GM to reduce the level of capital risk to the greatest extent.

4.3. Stable Strategy Analysis of CEs

The expected benefits of guarantee and of not guarantee by CEs are:

$$\begin{array}{ll}{U}_{31}=& xym{\Pi }_3+xy(1-m){\Pi }_7+x(1-y)m{\Pi }_{19}+x(1-y)(1-m){\Pi }_{23}+(1-x)ym{\Pi }_{35}+(1-x)y\\ & (1-m){\Pi }_{39}+(1-x)(1-y)m{\Pi }_{51}+(1-x)(1-y)(1-m){\Pi }_{55};\end{array}$$

(7)

$$\begin{array}{ll}{U}_{32}=& xym{\Pi }_{11}+xy(1-m){\Pi }_{15}+x(1-y)m{\Pi }_{27}+x(1-y)(1-m){\Pi }_{31}+(1-x)ym{\Pi }_{43}+(1-x)\\ & y(1-m){\Pi }_{47}+(1-x)(1-y)m{\Pi }_{59}+(1-x)(1-y)(1-m){\Pi }_{63}.\end{array}$$

(8)

Therefore, the replicator dynamic equation of CEs is:

$$F(z)=dz/dt=z({\mathrm{U}}_{31}-{\mathrm{U}}_3)=z(1-z)({\mathrm{U}}_{31}-{\mathrm{U}}_{32})=z(1-z)C(x,y,m)$$

(9)

where $C(x,y,m)=z(1-z)\{y[(m-1)({\mathrm{E}}_b-F+\Delta E_b^{″})+m({\mathrm{E}}_{g1}-{\mathrm{E}}_{g2})-C_c+(\sigma +(m-1)$$(1+r))D_1+x\lambda (1+r)D_1]+x(1-m)V_3\}$.

Let $x_0=\frac{y\{(m-1)(E_b-F+\Delta E_b^{″})+m(E_{g1}-E_{g2})-{\mathrm{C}}_c+[\sigma +(m-1)(1+r)]D_1\}}{(m-1){\mathrm{V}}_3-y\lambda (1+r)D_1}$, then

(1) when $x=x_0$, $F(z)\equiv 0$, so any $z\in [0,1]$ is a stable point;

(2) When $x\ne x_0$, according to $F(z)=0$, there are two zeros $z=0$ and $z=1$, that is, the CEs has two stable strategies, namely, “no guarantee” and “guarantee”.

Theorem 3.

When$0<x<x_0$, the stable strategy of CEs is “no guarantee”. When$x_0<x<1$, the stable strategy of CEs is “guarantee”.

For the proof of theorem 3, see Appendix A, “Proof of theorem 3”. Theorem 3 shows that the decline of the probability of strict supervision by the government will make the stable strategy of the CEs change from guarantee to no guarantee. Similarly, the increase in the probability of strict supervision by the government will change the stable strategy of CEs from no guarantee to guarantee. When the government adopts strict supervision strategy, CEs can get the risk compensation, and use that income to make up for the cost of supervising the production behavior of SMEs, which can increase the enthusiasm of it to guarantee. SMEs that fail to carry out GM when the CEs do not guarantee will be punished, and the CEs as the responsible enterprises of the SC will be affected. Therefore, if there is governmental strict supervision, the CEs will choose guarantee to help SMEs obtain GL from FIs and supervise their GM to reduce their losses. Otherwise, the CEs will not provide guarantee.

4.4. Stable Strategy Analysis of SMEs

The expected benefits $U_{41}$ of adopting GM and $U_{42}$ of do not adopting GM by SMEs are:

$$\begin{array}{ll}{U}_{41}=& xyz{\Pi }_4+xy(1-z){\Pi }_{12}+x(1-y)z{\Pi }_{20}+x(1-y)(1-z){\Pi }_{28}+(1-x)yz{\Pi }_{36}+(1-x)\\ & y(1-z){\Pi }_{44}+(1-x)(1-y)z{\Pi }_{52}+(1-x)(1-y)(1-z){\Pi }_{60};\end{array}$$

(10)

$$\begin{array}{ll}{U}_{42}=& xyz{\Pi }_8+xy(1-z){\Pi }_{16}+x(1-y)z{\Pi }_{24}+x(1-y)(1-z){\Pi }_{32}+(1-x)yz{\Pi }_{40}+(1-x)\\ & y(1-z){\Pi }_{48}+(1-x)(1-y)z{\Pi }_{56}+(1-x)(1-y)(1-z){\Pi }_{64}.\end{array}$$

(11)

Therefore, the replicator dynamic equation of SMEs is:

$$F(m)=dm/dt=m({\mathrm{U}}_{41}-{\mathrm{U}}_4)=m(1-m)({\mathrm{U}}_{41}-{\mathrm{U}}_{42})=m(1-m)D(x,y,z)$$

(12)

where $D(x,y,z)=F_m-D_0-R_b+S_h+y(D_0+R_{g2}-\Delta R_b^{″}-W)+x[(1-yz)T-y(1+r)(1-z)$ $D_2+y(1-z)V_2]+yz[2R_{g1}+V_1+F-(1+r)D_1+R_b-W-R_{g2}+\Delta R_b^{″}]$.

Let $x_0=\frac{F_m-D_0-R_b+S_h+y(D_0+R_{g2}-\Delta R_b^{″}-W)+yz[F+2R_{g1}+V_1-(1+r)D_1+R_b-W-R_{g2}+\Delta R_b^{″}]}{(yz-1)T+y(1-z)[(1+r)D_2-V_2]}$, then

(1) when $x=x_0$, $F(m)\equiv 0$, so any $m\in [0,1]$ is a stable point;

(2) When $x\ne x_0$, according to $F(m)=0$, there are two zeros $m=0$ and $m=1$, namely, SMEs have stable strategies of “do not adopt GM” and “adopt GM”.

Theorem 4.

When$0<x<x_0$, the SMEs stable strategy is “not adopt GM”. When$x_0<x<1$, the SMEs stable strategy is “adopt GM”.

For the proof of theorem 4, see Appendix A, “Proof of theorem 4”. Theorem 4 shows that the decline of the probability of strict supervision by the government will change the stable strategy of SMEs from adopting GM to not adopting GM. Similarly, the increase in the probability of strict supervision by the government will change the stable strategy of SMEs from not adopting GM to adopting GM. When the government adopts strict supervision, SMEs will be punished by the government because they do not adopt GM, resulting in a lot of losses. In addition, when the government implements strict supervision, CEs can obtain risk compensation, which greatly promotes the enthusiasm of CEs to provide guarantee for SMEs. Guarantee means CEs have the responsibility to supervise the production behavior of SMEs. Due to the information symmetry, the CE is bound to find the non-green production management behavior of SMEs, and SMEs will also be expelled from the SC and lost their future expected earnings because they fail to keep their promises. Therefore, when the government adopts strict supervision, SMEs will choose to adopt GM for the consideration of maximizing their own interests.

5. Stability Analysis of Strategy Combination

According to the replicator dynamic equation, the quadripartite EG replicator dynamic system of GSCF system is constructed:

$$\{\begin{array}{l}F(x)=x(x-1)A(y,z,m)\\ F(y)=y(1-y)B(x,z,m)\\ F(z)=z(1-z)C(x,y,m)\\ F(m)=m(1-m)D(x,y,z)\end{array}$$

(13)

Theorem 5.

There are 16 groups of pure strategy balancing strategy combinations in the quadripartite EG replicator dynamic system of GSCF.

For the proof of theorem 5, see Appendix A, “Proof of theorem 5”.

Next, the stability of 16 groups of pure strategy equilibrium in the quadripartite game replicator dynamic system of GSCF is discussed by using Lyapunov’s first law. The Jacobian matrix of this system is obtained as follows:

$$J=\left[\begin{array}{l}\frac{\partial F(x)}{\partial x}\frac{\partial F(x)}{\partial y}\frac{\partial F(x)}{\partial z}\frac{\partial F(x)}{\partial m}\\ \frac{\partial F(y)}{\partial x}\frac{\partial F(y)}{\partial y}\frac{\partial F(y)}{\partial z}\frac{\partial F(y)}{\partial m}\\ \frac{\partial F(z)}{\partial x}\frac{\partial F(z)}{\partial y}\frac{\partial F(z)}{\partial z}\frac{\partial F(z)}{\partial m}\\ \frac{\partial F(m)}{\partial x}\frac{\partial F(m)}{\partial y}\frac{\partial F(m)}{\partial z}\frac{\partial F(m)}{\partial m}\end{array}\right]$$

(14)

Based on the Jacobian matrix, the corresponding eigenvalues of 16 groups of pure strategy of equilibrium strategy combination and their positive and negative symbols are shown in

Table 3. Stability analysis of pure strategy combination.

Pure Strategy Combination	$\mathbf{Eigenvalues}{\mathit{\lambda }}_1,{\mathit{\lambda }}_2,{\mathit{\lambda }}_3,{\mathit{\lambda }}_4$	Plus and Minus Sign	Stability
(0,0,0,0)	$0,(r-r_0)D_2-C_f$ $,F_m-D_0-R_b+S_h$ $,T-C_g+U_g+\beta D_2$	(0,−,X,X)	uncertainty
(1,0,0,0)	$V_3$ $,C_g-T-U_g-\beta D_2$ $,F_m-D_0-R_b+S_h+T$ $,(\alpha -1+\beta -r-r_0)D_2-C_f$	(+,X,X,X)	unstable
(0,1,0,0)	$C_f-(r-r_0)D_2$ $,T-C_g+U_g-\alpha D_2$ $,F_m-R_b+R_{g2}+S_h-W-\Delta R_b^{″}$ $,F-D_1-E_b-C_c-\Delta E_b^{″}+(\sigma -r)D_1$	(+,X,X,X)	unstable
(0,0,1,0)	$0,(r-r_0)D_1$ $,F_m-D_0-R_b+S_h$ $,T-C_g+U_g+\beta D_1$	(0,−,X,X)	uncertainty
(1,1,0,0)	$C_g-T-U_g+\alpha D_2$ $,C_f+(1-\alpha -\beta +r+r_0)D_2$ $,F-E_b-C_c-\Delta E_b^{″}+[\lambda +\sigma -r(1-\lambda )-1]D_1$ $,F_m-R_b+R_{g2}+S_h+T+V_2-W-\Delta R_b^{″}-(1+r)D_2$	(X,+,X,X)	unstable
(1,0,1,0)	$-V_3$ $,C_g-T-U_g-\beta D_1$ $,(\alpha +\beta +r-r_0)D_1$ $,F_m-D_0-R_b+S_h+T$	(−,−,X,X)	uncertainty
(0,1,1,0)	$(r_0-r)D_1$ $,U_g-C_g-[\alpha +\lambda (1+r)]D_1$ $,C_c+E_b-F+\Delta E_b^{″}+(1-\sigma +r)D_1$ $,F+F_m+2R_{g1}+S_h+V_1-2W-(1+r)D_1$	(+,X,X,X)	unstable
(1,1,1,0)	$(r_0-\beta -r-\alpha )D_1$ $,C_g-U_g+[\alpha +\lambda (1+r)]D_1$ $,F+F_m+2R_{g1}+S_h+V_1-2W-(1+r)D_1$ $,C_c+E_b-F-V_3+\Delta E_b^{″}+[1-\lambda -\sigma +r(1-\lambda )]D_1$	(X,X,X,X)	ESS (satisfy condition 1)
(0,0,0,1)	$0,(r-r_0)D_2-C_f$ $,U_g-C_g+\beta D_2$ $,D_0-F_m+R_b-S_h$	(0,−,X,X)	uncertainty
(1,0,0,1)	$0,C_g-U_g-\beta D_2$ $,D_0-F_m+R_b-S_h-T$ $,(\alpha +\beta +r-r_0)D_2-C_f$	(0,X,X,X)	uncertainty
(0,1,0,1)	$U_g-C_g-\alpha D_2$ $,C_f+(r_0-r)D_2$ $,E_{g1}-C_c-E_{g2}+\sigma D_1$ $,R_b-F_m-R_{g2}-S_h+W+\Delta R_b^{″}$	(X,+,X,X)	unstable
(0,0,1,1)	$0,(r-r_0)D_1$ $,U_g-C_g+\beta D_1$ $,D_0-F_m+R_b-S_h$	(0,−,X,X)	uncertainty
(1,1,0,1)	$C_g-U_g+\alpha D_2$ $,C_f+(-\alpha -\beta -r+r_0)D_2$ $,E_{g1}-C_c-E_{g2}+[\lambda (1+r)+\sigma ]D_1$ $,(1+r)D_2-F_m+R_b-R_{g2}-S_h-T-V_2+W+\Delta R_b^{″}$	(X,X,X,X)	ESS (satisfy condition 2)
(1,0,1,1)	$0,C_g-U_g-\beta D_1$ $,(\alpha +\beta +r-r_0)D_1$ $,D_0-F_m+R_b-S_h-T$	(0,X,X,X,)	uncertainty
(0,1,1,1)	$(r_0-r)D_1$ $,C_c-E_{g1}+E_{g2}-\sigma D_1$ $,U_g-C_g-[\alpha +\lambda (1+r)]D_1$ $,(1+r)D_1-F-F_m-2R_{g1}-S_h-V_1+2W$	(+,−,X,X)	unstable
(1,1,1,1)	$(r_0-\beta -r-\alpha )D_1$ $,C_g-U_g+[\alpha +\lambda (1+r)]D_1$ $,C_c-E_{g1}+E_{g2}-[\sigma +\lambda (1+r)]D_1$ $,(1+r)D_1-F-F_m-2R_{g1}-S_h-V_1+2W$	(X,X,X,X)	ESS (satisfy condition 3)

Note: X represents the inability to determine the positive or negative eigenvalues. Condition (1): $r_0-\beta <r+\alpha$, $U_g-C_g-\alpha D_1-\lambda (1+r)D_1>0$, $R_{g1}-W+S_h-(1+r)D_1<-R_{g1}+W-F_m-F-V_1$, $E_b+\Delta E_b^{″}-V_3<[\sigma +(\lambda -1)(1+r)]D_1-C_c+F$; condition (2): $U_g-C_g-\alpha D_2>0$, $(r_0-\beta )D_2<(r+\alpha )D_2-C_f$, $E_{g1}+[\sigma +\lambda (1+r)]D_1-C_c<E_{g2}$, $R_b+\Delta R_b^{″}-T-V_2-F_m<R_{g2}-W-(1+r)D_2+S_h$; condition (3): $r_0-\beta <r+\alpha$, $U_g-C_g-[\alpha +\lambda (1+r)]D_1>0$, $E_{g1}+[\sigma +\lambda (1+r)]D_1-C_c>E_{g2}$, $-R_{g1}+W-F_m-F-V_1<R_{g1}-W+S_h-(1+r)D_1$.

.

Theorem 6.

There are three possible ESS in the system. When condition (1) is satisfied, (1,1,1,0) is ESS. When condition (2) is satisfied, (1,1,0,1) is ESS. When condition (3) is satisfied, (1,1,1,1) is ESS.

For the proof of theorem 6, see Appendix A, “Proof of theorem 6”. The three ESS (1,1,1,0), (1,1,0,1), and (1,1,1,1) are all achieved under the strict supervision of government departments, indicating that the smooth development of GSCF business need the government’s participation. For scenario 1 (1, 1, 1, 0), although the government strictly supervises and FIs provide GL to SMEs under the guarantee of CEs, the extra cost of adopting GM is too large, so that the benefits of adopting GM are less than those of not adopting GM, namely, $R_{g1}-W+S_h-(1+r)D_1<-R_{g1}+W-F_m-F-V_1$, so SMEs tend not to adopt GM. To achieve the ideal stable state of scenario 3 (1,1,1,1), it is necessary for CEs to increase the penalty on SMEs when compensating for GL and the resulting loss of expected future earnings of SMEs. The government can increase the industry’s recognition of green production through market regulation, thus increasing the negative effects of non-green management of SMEs and forcing them to adopt GM as agreed. For scenario 2 (1,1,0,1), the guarantee income is still less than the non-guarantee income due to the high supervision cost in the case of the CE’s guarantee, namely, $E_{g1}+[\sigma +\lambda (1+r)]D_1-C_c<E_{g2}$.Therefore, CEs prefer non-guarantee strategy. To achieve the stable ideal state of scenario 3, the government departments need to increase the risk compensation for the CE’s guarantee to make up for the excessive supervision cost.

6. Numerical Simulations

In this section, MATLAB is used for simulation to study the impact of different parameters on the strategy evolution results. From the above analysis, (1,1,1,1) indicates that under the strict supervision of the government, all subjects of the SCF system interact positively, helping SMEs to adopt GM, and the EG system reaches an ideal stable state. In order to show the evolution path of quadripartite game strategy selection of government departments, FIs, CEs, and SMEs in more detail, the evolution of strategy selection is simulated under the state (1,1,1,1). According to the actual situation, the parameter values are estimated and set as follows: $W=12$, $R_{g1}=40$, $E_{g1}=45$, $E_{g2}=35$, $D_1=23$, $r=0.06$, $r_0=0.08$, $C_g=1$, $\alpha =0.08$, $\beta =0.1$, $\sigma =0.1$, $\lambda =0.2$, $C_c=4$, $F=1$, $V_1=5$, $S_h=1$, $F_m=1$, $U_g=10$. At this time, condition (3) is satisfied. Therefore, under the circumstance that government departments implement strict supervision strategy, namely, $x=1$, the evolutionary path of strategy selection of FIs, CEs, and SMEs is shown in Figure 1. The whole system reaches the ideal state of (1,1,1,1).

6.1. Impact of Strict Supervision Costs on Government

When the government carries out strict supervision, it can reduce the harm to the environment caused by SMEs because they do not adopt GM, but the government needs to pay extra supervision costs in strict supervision. Keep other parameters unchanged and set strict supervision costs $C_g$ as 0.5, 1.0, 2.0, and 2.5, respectively. Figure 2 displays the evolutionary path of government department policy selection.

As can be seen from Figure 2, as the cost increases, the time for government departments to finally choose “strict supervision” gradually increases. The main reason is that excessive supervision costs will cause serious financial and human burdens, and the government is more inclined not to carry out all-out strict supervision when it weighs the income and expenditure. Therefore, the increase of supervision costs has a negative impact on the government’s supervision behavior. In view of this phenomenon, on the one hand, an online comprehensive information query platform can be built to integrate the trade, financial, and environmental information of FIs, and industrial and commercial enterprises, so as to reduce the loan costs and risks of FIs, and formulate a GSCF loan encouragement mechanism for FIs to enhance the enthusiasm of it to issue GL to SMEs. On the other hand, the incentive risk compensation mechanism should be developed for CEs providing guarantee, and the advantage of information symmetry between the CEs and SMEs should be used to reduce the cost of strict supervision by the government.

6.2. Impact of Future Expected Benefits on CEs and SMEs

When CEs provide loan guarantees for SMEs, SMEs will lose the future expected benefits due to the dishonest behavior. In order to observe the impact of future expected benefits $V_1$ on CEs and SMEs, setting $V_1$ as 5, 50, 200, and 500, respectively. The evolution path of strategy selection of SMEs and CEs over time is shown in Figure 3 and Figure 4.

As can be seen from Figure 3, with the increase of $V_1$, the time for SMEs to finally evolve to “adopt GM” strategy is gradually shortened, and the speed of stable decision-making is constantly accelerated. This indicates that when the expected future income is large, SMEs will increase their willingness to “adopt GM” according to the agreement. It can be seen that the increase in the purchase business volume from the CEs has a certain incentive effect on the production behavior of SMEs. Further observation of Figure 4 shows that when SMEs tend to adopt GM strategies faster, CEs tend to guarantee faster, and the probability of initial non-guarantee also decreases. This is because when CEs place a large number of continuous business orders to SMEs, it tends to abide by the agreement and carry out GM in order to maintain such a stable cooperative relationship. Considering this situation, CEs will try their best to provide guarantee for SMEs in order to help them obtain more loans and to ensure the continuity of SC business and profit.

6.3. Impact of Loan Compensation and No Loan Penalty on FIs

Under the strict supervision of government departments, FIs will be punished if they do not loan, while they can get subsidies if they loan. To observe the influence of penalty $\beta$ and compensation $\alpha$ on the strategy selection of FIs, values of $\alpha$ and $\beta$ are 0.01, 0.03, 0.06, 0.08, respectively. The evolution path of FIs’ strategy selection over time is shown in Figure 5 and Figure 6.

As can be seen from Figure 5, with the increase $\alpha$, the speed of FIs’ evolution to the stable strategy of “loan” is accelerate. It can be seen that when no loan will suffer a large business penalty, giving FIs appropriate subsidies to make up for the loss of business income due to giving up traditional commercial loans can promote FIs to choose “loan”. As can be seen from Figure 6, with the increase of $\beta$, the speed of FIs’ evolution to “loan” accelerates. It can be seen that when giving FIs large compensation, and appropriate punishment for not loan, FIs can be encouraged to choose “loan”. Therefore, the implementation of GSCF loan business of FIs with large business punishment supplemented by appropriate business compensation, or large business compensation supplemented by appropriate business punishment, can prompt it to finally choose loan, then inject capital vitality for the adoption of GM by SMEs in the SC.

In order to study the relationship between compensation and punishment, $\alpha$ and $\beta$ are respectively valued as shown in Figure 7. According to condition (3) $r_0-\beta <r+\alpha$, that is, if $\beta >0.02-\alpha$, FIs will tend to choose “loan”. Scene 1 and Scene 2 satisfy, so they eventually evolve into an ideal stable state of “loan”; scene 3 and scene 4 do not satisfy, so they eventually evolve into an unsatisfactory stable state of “no loan”, which is consistent with the theoretical reasoning results. Therefore, when implementing the business subsidy and punishment mechanism for FIs, a larger business penalty should be supplemented by a smaller business subsidy, and the business subsidy should be the difference between the traditional commercial loan and GL business income of GSCF.

6.4. Impact of Positive Industry Benefits on SMEs

When SMEs adopt GM to establish a positive image of the industry, the order volume and wholesale price will increase accordingly, so as to obtain the positive industry benefits $S_h$. Setting $S_h$ as 0, 10, 50, and 100, respectively. The evolution path of SMEs’ strategy selection over time is shown in Figure 8.

As can be seen from Figure 8, with $S_h$ rising from 0 to 100, the time and speed for SMEs to reach the ideal strategy of “adopt GM” are accelerating. This is mainly because when SMEs adopt GM, they are recognized by the industry, and the increase in order volume and wholesale price can bring more benefits to it. Therefore, the GM behavior of SMEs can establish a positive corporate image for themselves and thus enhance their own value. Therefore, on the one hand, the government should encourage CEs to carry out green procurement, so as to force SMEs to adopt GM. On the other hand, the government can strengthen market regulation, force the industry to follow the green production mode by increasing the probability of limiting and stopping production, increasing pollution fines and other methods, and improve the industry’s acceptance of green products.

7. Conclusions

7.1. Results

First, the government’s participation can effectively promote the sustainable development of SCF. There are three situations in the final stable strategy combination of EG, all of which are achieved under the strict supervision of the government. Therefore, the government’s participation in the sustainable development of SCF is effective. This is consistent with the conclusion of Shan [51]. This is because strict supervision by the government will punish SMEs that cause environmental pollution, reward and punish FIs that carry out GL business, and compensate the CEs for risk. All the intervention measures of the government will have an impact on the income of the game participants, and then influence the final strategic choice of the participants to evolve in a positive direction, and promote the sustainable development of SCF.

Second, for government departments, the cost of strict supervision will negatively affect their supervision behavior. This is consistent with the views of He [49]. The results show that the greater the cost of strict supervision, the longer it takes the government to achieve the stable strategy of “strict supervision”. In the case of strict supervision, the government will give incentives and risk compensation to the active participants of GSCF business, which will increase the government expenditure, so the higher the cost, the more inclined the government will not carry out strict supervision. SMEs that do not adopt GM positively affects the government’s supervision behavior. This is consistent with the views of Xu et al. [52]. The more SMEs tend not to adopt GM, the more likely the government is to implement strict supervision strategies to encourage FIs to provide financial support for their GM behavior and encourage CEs to provide guarantee for their loan behavior, so as to reduce the environmental damage caused by non-green production management and promote the sustainable development of SCF.

Third, for FIs, the government simultaneously implements large penalties for non-lending and subsidies similar to the profit difference between traditional commercial loan and GL, which can motivate them to provide GL to the greatest extent. The stability analysis showed that when the sum of rewards and penalties is greater than the difference between traditional commercial loan and GL, the final strategy of FIs stabilizes in the ideal state of loans. As interest rates on GL are lower than those on traditional commercial loan, FIs, as profit-making organizations, lack the incentive to provide GL to SMEs. The original intention of the government’s participation in GSCF is to encourage FIs to issue GL to SMEs, rather than seeking benefits for themselves by imposing penalties. The simultaneous imposition on FIs of large penalties and subsidies to cover losses in their operations means that appropriate subsidies, with a deterrent, can achieve good results.

Fourth, for CEs, the guarantee risk compensation from the government can effectively encourage them to choose guarantee. This is consistent with the conclusion of Feng [32]. The results show that strict supervision by the government can compensate the risk of the CEs and promote it to choose the guarantee strategy. The CEs guarantee the loan business of SMEs and assume the responsibility to repay the loan on behalf of them. In order to reduce their own losses, CEs tend to supervise the loan commitments of SMEs, so they will pay some supervision costs. Excessive supervision cost will reduce the enthusiasm of CEs to provide guarantee, so appropriate risk compensation is particularly necessary. The stability of SC cooperation can also encourage CEs to provide guarantees for SMEs to gain more profits. This is because close cooperation between CEs and SMEs can increase mutual trust, and SC can be disrupted if SMEs suffer production difficulties due to lack of funds. If CEs provide guarantees to SMEs that have stable cooperation, they will not only help SMEs obtain loans to produce on schedule, but also help them earn more profits.

Fifth, for SMEs, the perceived expected return of SC positively affects their GM behavior. The results show that the larger the expected income, the shorter and faster the time for SMEs to achieve the ideal strategy of “adopting GM”. SMEs have unstable income due to the unstable source of customers. If SMEs in the SC have stable customers, stable trading volume, stable SC cooperation, and greater perceived benefits in the future, then SMEs will try their best to avoid default behavior to maintain this stable relationship. This is consistent with the conclusion of Wang et al. [31]. The positive effect of GM can also improve the enthusiasm of SMEs to adopt GM. Enterprises reduce environmental pollution, carry out GM, and produce green products, which can establish a positive image of enterprises and increase industry recognition, which can bring an increase in customers and orders.

7.2. Suggestions

Based on the above research results, the following policy recommendations are proposed to promote the sustainable development of SCF:

First, build an online comprehensive platform system of GSCF with the help of digital technology to reduce the cost of business development. Strict supervision by the government, loans from FIs, and guarantees from CEs all require information costs, which will affect their choice of positive GSCF strategies. The online comprehensive platform system collects the operational, financial, and pollutant discharge information of FIs and enterprises, can greatly reduce the information asymmetry between participants, and the cost of business development, and promote participants to choose active strategies. However, the establishment of an information system with the help of digital technology also needs to think about how to pay the cost, how to apportion the cost, and whether the participants are willing to obey the apportionment.

Second, government departments should formulate a GL reward and punishment mechanism with a relatively high punishment and appropriate subsidy. According to the results, when the sum of business rewards and penalties is greater than the income difference between traditional commercial loans and GLs, FIs finally stabilize in the loan strategy. However, the income difference is fixed, so high penalties and appropriate rewards can stimulate the enthusiasm of FIs to participate in a GSCF loan business. However, higher penalties tend to give the government the perverse effect of seeking its own personal gain.

Third, government departments may appropriately increase the risk compensation for the CE’s guarantee of GSCF business. CEs make use of the dominant position of SC to make themselves in a state of information symmetry with SMEs. CEs of guarantee will supervise SMEs to reduce their own risk losses, and the supervision cost will in turn affect the enthusiasm of CEs to adopt guarantee. Therefore, governments give appropriate risk compensation, so as to make up for the cost of supervision of CEs, and maximize the use of the information symmetry between CEs and SMEs to prevent the damage to the environment caused by SMEs’ failure to adopt GM. This measure has the effect of saving costs and a better supervision effect on the management behavior of SMEs, but it needs to pay attention to prevent collusion between CEs and SMEs.

Fourth, CEs may increase the amount of green products purchased from SMEs. The increase in the purchase volume enables SMEs to have stable and considerable sources of income, which can increase their perception of the expected income of the SC and reduce the occurrence of default behaviors. The implementation of this measure requires CEs to fully consider the production capacity of SMEs and help them solve production problems, otherwise, the SC will be interrupted, so the strength of CEs will be highly required.

Fifth, government departments may carry out market regulation to increase the recognition of green products and strengthen the punishment of non-green production behavior. According to the results, the positive effects of green production, including the increase of customers and orders, can shorten the time for SMEs to adopt the ideal stable strategy of GM. Therefore, the regulation and punitive measures imposed by the government can increase the market’s recognition of green products and encourage SMEs to actively adopt GM to bring more industrial benefits for themselves. However, the implementation of this strategy will increase the costs of the government.

7.3. Limitation of Research

We recognize that in the process of model construction, it is assumed that when SMEs are fined by government departments, the fine amount is greater than their earnings. However, in reality, some of the earnings of SMEs suffering from fines may be used to repay the loans of financial institutions, and not all of the loans will be repaid by the guaranteed CEs. Therefore, in future studies, we plan to establish a more comprehensive model by comparing partial compensation and total compensation of CEs.