*4.1. Basic Assumptions*

According to the game relationship between the focus governmen<sup>t</sup> and the non-focus governmen<sup>t</sup> in green governance, the following assumptions are put forward:


a. In the knowledge learning effect, the green governance willingness level (tacit knowledge level) of focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> is *E*1 and *E*2, respectively. The reality is characterized by internal meetings of local governments on green communication, media campaigns on green governance, etc. When they transform knowledge, they are influenced by each other's will. The incentive coefficients of focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> are *a*1 and *a*2, respectively. Indicates the frequency and acceptance of interaction between the parties in reality. Due to the knowledge base gap, non-focus governmen<sup>t</sup> needs to effectively perceive tacit knowledge in the process of 'learning' from the focus government, so the perception coefficient of the learning effect of non-focus governmen<sup>t</sup> is set as *c*.

b. In the knowledge spillover effect, the knowledge stock (explicit knowledge level) of green governance of focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> is *K*1 and *K*2, respectively. The reality is characterized by green summary reports and green experiences of local governments. When the two sides interact with each other, they absorb the spillover part of the managemen<sup>t</sup> experience (government managemen<sup>t</sup> ability, planning arrangement, etc.) to acquire the other side's knowledge. The knowledge spillover effect among subjects is affected by the proportion of complementary knowledge among subjects, the degree of knowledge protection, the ability of autonomous learning, and the ability of transformation and landing [57]. It is assumed that the proportion of complementary knowledge between focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> is *α*1 and *α*2, the degree of knowledge protection is *β*1 and *β*2, the coefficient of autonomous learning ability is *λ*1 and *λ*2, and the ability of knowledge transformation is *θ*1 and *θ*2.

c. Under the influence of the knowledge learning effect and knowledge spillover effect, focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> construct the knowledge collaborative network of green governance, forming the knowledge collaborative effect. Let *h* and *i* be the elasticity coefficients of complementary knowledge stock shared by focus governmen<sup>t</sup> and non-focus government, respectively, and *h* + *i* = 1. The perceived relationship of trust between the two sides will affect the knowledge synergy effect. The learning effect perception coefficient *c* reflects the perception relationship. The knowledge synergy effect benefit created by the focus governmen<sup>t</sup> and the non-focus governmen<sup>t</sup> is *<sup>c</sup>*(*<sup>α</sup>*1*K*1) *h* (*<sup>α</sup>*2*K*2) *i* . In the repeated game of knowledge coordination, the focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> will also be affected by the knowledge reciprocity effect [58]. The open part of the knowledge system realizes the cooperative value added to the original knowledge system through knowledge interaction. Assuming that *ξ* is the cooperative value-added coefficient, the reciprocal effect of knowledge is inversely proportional to the degree of knowledge protection.

Based on the second hypothesis, we ge<sup>t</sup> that the benefits of the knowledge learning effect of the focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> are *E*2*a*1 and *<sup>E</sup>*1(*<sup>a</sup>*2 + *c*), respectively. The return of the knowledge spillover effect income is *<sup>K</sup>*2*α*2(<sup>1</sup> − *β*2)*<sup>λ</sup>*1*K*1*θ*1 and *<sup>K</sup>*1*α*1(<sup>1</sup> − *β*1)*<sup>λ</sup>*2*K*2*θ*2. Because of the difference of regional foundation and the knowledge synergy effect input, the income of the knowledge synergy effect is not evenly distributed but determined by the proportion of knowledge synergy effect income distribution *z*1 and *z*2. Therefore, the income of the focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> through the knowledge synergy effect is *<sup>z</sup>*1*<sup>c</sup>*(*<sup>α</sup>*1*K*1) *h* (*<sup>α</sup>*2*K*2) *i* and *<sup>z</sup>*2*<sup>c</sup>*(*<sup>α</sup>*1*K*1) *h* (*<sup>α</sup>*2*K*2) *i*, respectively. In the knowledge reciprocity effect, the focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> obtain value-added benefits, which are *<sup>K</sup>*1(<sup>1</sup> − *β*1)*ξ* and *<sup>K</sup>*2(<sup>1</sup> − *β*2)*ξ*, respectively.


value-added benefits of self-governance: Δ *K*1*λ*1*θ*1, Δ *K*2*λ*2*θ*2, where Δ *K*1, Δ *K*2 are the knowledge increments obtained by both sides through focused learning. Because of the idle spillover knowledge resources and knowledge closure, the focus government and non-focus governmen<sup>t</sup> will lose the opportunity of spillover knowledge: *<sup>K</sup>*1(<sup>1</sup> − *β*1)*<sup>γ</sup>*11, *<sup>K</sup>*2(<sup>1</sup> − *β*2)*<sup>γ</sup>*21. *γ*11. *γ*21 is the opportunity loss coefficient of the focus governmen<sup>t</sup> and non-focus government, respectively. The focus governmen<sup>t</sup> and the non-focus governmen<sup>t</sup> are punished for the loss of knowledge protection: *K*1*β*1*γ*12 and *K*2*β*2*γ*22. *γ*12 and *γ*22 are the penalty coefficients of knowledge protection for the focus governmen<sup>t</sup> and non-focus government, respectively.

• There are external constraints in knowledge management. When the focus governmen<sup>t</sup> actively leads and the non-focus governmen<sup>t</sup> actively participates in green governance, the central governmen<sup>t</sup> will give corresponding incentive support *Rg*1 and *Rg*2. The central governmen<sup>t</sup> tries its best to promote the integration of regional green development. When the non-focus governmen<sup>t</sup> has the will to actively participate and the focus governmen<sup>t</sup> governs independently, it will give the focus governmen<sup>t</sup> *F* punishment. The focus governmen<sup>t</sup> will eliminate the backward industries to the non-focus government, so the focus governmen<sup>t</sup> will ge<sup>t</sup> the industry elimination income *G*1, and the non-focus governmen<sup>t</sup> will ge<sup>t</sup> the industry transfer income *G*2. Considering the lack of the initial development ability of the non-focus government, when the focus governmen<sup>t</sup> actively leads and the non-focus governmen<sup>t</sup> governs independently, the central governmen<sup>t</sup> will not punish the non-focus governmen<sup>t</sup> temporarily. Any party who refuses to cooperate in governance will suffer credit loss *T*.

#### *4.2. Payment Matrix and Dynamic Equation of Replication*

When the focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> are positive peers, the corresponding strategy combination is active leadership and active participation. Each subject realizes the internal and external transformation of knowledge, keeps the internal knowledge benefits, and undertakes the cost of the knowledge learning effect, knowledge spillover effect and knowledge spillover effect. Each subject obtains the benefits of the knowledge learning effect, knowledge spillover effect, knowledge synergy effect, knowledge reciprocity effect, and the incentive support given by the central government. In the case of negative peers corresponding to the combination of strategies of autonomous governance and autonomous governance, knowledge only transforms internally. Each subject undertakes the opportunity to lose spillover knowledge and the penalty loss of knowledge protection, gains internal knowledge benefits, and gains value-added benefits through self-governance. In the case of consistent direction peers, the strategy combination is autonomous governance and active participation. The focus governmen<sup>t</sup> bears the loss of knowledge opportunity and knowledge protection punishment and suffers from external punishment and reputation loss, but gains internal knowledge income, value-added income, and industry elimination income. At this time, the non-focus governmen<sup>t</sup> bears the cost of the knowledge learning effect and knowledge spillover effect. Because the cooperative relationship cannot be constructed, it can only obtain internal knowledge benefits, industrial transfer benefits, and the central government's incentive. In the case of reverse peers, the corresponding strategy combination is active leadership and autonomous governance. The focus governmen<sup>t</sup> bears the cost of knowledge learning and spillover. Because of the blocking of knowledge transformation, they only gain internal knowledge benefits and incentive benefits. The non-focus governmen<sup>t</sup> loses the knowledge opportunity income and bears the punishment of knowledge protection and faces the reputation loss but gains the internal knowledge income and value-added income.

According to the above assumptions and the profit and loss analysis, the paymen<sup>t</sup> matrix of the game is obtained, as shown in Table 1.


**Table 1.** Payment matrix of the game between the Non-focus governmen<sup>t</sup> and non-focus government.

> According to the revenue matrix in Table 1, we can calculate the expected revenue and average revenue when the focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> choose different strategies. The expected benefits of active leadership *U*11, autonomous governance *U*12, and average income *U*1 of the focus governmen<sup>t</sup> can be expressed as:

$$\begin{aligned} \mathcal{U}\_{11} &= y[E\_2a\_1 + K\_2\mathbf{a}(1-\beta\_2)\lambda\_1\mathbf{K}\_1\theta\_1 + z\_1\mathbf{c}(a\_1\mathbf{K}\_1)^\dagger(a\_2\mathbf{K}\_2)^\dagger + (\mathbf{K}\_1 + \mathbf{E}\_1)\mathbf{R}\_1 + \mathbf{R}\_{\frac{3}{2}1} + \mathbf{K}\_1(1-\beta\_1)\mathbf{\bar{s}} - m\_1\mathbf{E}\_1 - \mathbf{K}\_1(b\_1+d\_1) - n\_1a\_1\mathbf{K}\_1] + \mathbf{R}\_{\frac{3}{2}1} + \mathbf{R}\_{\frac{3}{2}1} + \mathbf{R}\_{\frac{3}{2}1} + \mathbf{R}\_{\frac{3}{2}1} + \mathbf{R}\_{\frac{3}{2}1} + \mathbf{R}\_{\frac{3}{2}1}] \\ &+ (1-y)[(\mathbf{K}\_1 + \mathbf{E}\_1)\mathbf{R}\_1 + \mathbf{R}\_{\frac{3}{2}1} - K\_1(b\_1+d\_1) - m\_1\mathbf{E}\_1] \end{aligned}$$

$$\mathcal{U}\_{12} = y[(K\_1 + E\_1)R\_1 + G\_1 + \Delta K\_1 \lambda\_1 \theta\_1 - F - T - K\_1(1 - \beta\_1)\gamma\_{11} - K\_1 \theta\_1 \gamma\_{12}] + (1 - y)[(K\_1 + E\_1)R\_1 + \Delta K\_1 \lambda\_1 \theta\_1 - K\_1(1 - \beta\_1)\gamma\_{11} - K\_1 \theta\_1 \gamma\_{12}] + (1 - y)[(K\_1 + E\_1)R\_1 + \Delta K\_1 \lambda\_1 \theta\_1 - K\_1 \theta\_1 \gamma\_{11}] + (1 - y)[(K\_1 + E\_1)R\_1 + \Delta K\_1 \lambda\_1 \theta\_1 - K\_1 \theta\_1 \gamma\_{12}] + (1 - y)[(K\_1 + E\_1)R\_1 + \Delta K\_1 \lambda\_1 \theta\_1 - K\_1 \theta\_1 \gamma\_{11}] + (1 - y)[(K\_1 + E\_1)R\_1 + \Delta K\_1 \lambda\_1 \theta\_1 - K\_1 \theta\_1 \gamma\_{12}]$$

$$\mathcal{U}\_1 = \mathbf{x} \mathcal{U}\_{11} + (1 - \mathbf{x}) \mathcal{U}\_{12}$$

Similarly, the expected benefits of non-focus governmen<sup>t</sup> *U*21 (active participation), *U*22 (autonomous governance), and *U*2 (average benefits) can be expressed as follows

$$\begin{array}{rcl} \text{L\u021} &=& \text{x} [\text{E}\_1(a\_2+c)+\text{K}\_1\text{u}(1-\beta\_1)\lambda \text{z}\text{K}\_2\text{y}2\_2+\text{z}\text{z}\text{z}(a\_1\text{K}\_1)^\text{k}(\text{u}\text{z}\text{K}\_2)^\text{l}+(\text{K}\_2+\text{E}\_2)\text{R}\_2+\text{R}\_{\text{f2}}+\text{K}\_2(1-\beta\_2)\mathsf{f}-\mathsf{m}\_2\mathsf{E}\_2-\text{K}\_2(\mathsf{b}\_2+d\underline{\eta})-\mathsf{m}\_2\mathsf{u}\mathsf{E}\_2[\mathsf{v}\text{R}\_2\text{u}] \\ &+(1-\mathbf{x})[(\text{K}\_2+\text{E}\_2)\mathsf{R}\_2+\text{G}\_2+\text{R}\_{\text{f2}}-\text{K}\_2(\mathsf{b}\_2+d\underline{\eta})-\mathsf{m}\_2\mathsf{E}\_2] \end{array}$$

$$\mathcal{U}\_{22} = \mathbf{x}[(K\_2 + E\_2)R\_2 + \Lambda K\_2 \lambda\_2 \theta\_2 - T - K\_2(1 - \beta\_2)\gamma\_{21} - K\_2 \beta\_2 \gamma\_{12}] + (1 - \mathbf{x})[(K\_2 + E\_2)R\_2 + \Lambda K\_2 \lambda\_2 \theta\_2 - K\_2(1 - \beta\_2)\gamma\_{21} - K\_2 \beta\_2 \gamma\_{22}]$$

$$\mathcal{U}\_2 = y\mathcal{U}\_{21} + (1 - y)\mathcal{U}\_{22}$$

From the above expressions, the replication dynamic equations of the focus government and non-focus governmen<sup>t</sup> can be calculated.

The dynamic replication equation of the focus government's choice of active leadership strategy is as follows:

*<sup>F</sup>*(*x*) = *dxdt* = *<sup>x</sup>*(*<sup>U</sup>*11 − *<sup>U</sup>*1) = *x*(<sup>1</sup> − *<sup>x</sup>*)*y*[*<sup>E</sup>*2*a*1 + *<sup>K</sup>*2*α*2(<sup>1</sup> − *β*2)*<sup>λ</sup>*1*K*1*θ*1 + *<sup>z</sup>*1*<sup>c</sup>*(*<sup>α</sup>*1*K*1)*<sup>h</sup>*(*<sup>α</sup>*2*K*2)*<sup>i</sup>* + *<sup>K</sup>*1(<sup>1</sup> − *β*1)*ξ* −*n*1*α*1*K*<sup>1</sup> − *G*1 + *F* + *<sup>T</sup>*]+[*Rg*1 − *<sup>K</sup>*1(*b*1 + *d*1) − *<sup>m</sup>*1*E*1 − Δ*K*1*λ*1*θ*1 + *<sup>K</sup>*1(<sup>1</sup> − *β*1)*<sup>γ</sup>*11 + *<sup>K</sup>*1*β*1*γ*12]

The dynamic replication equation of the non-focus government's choice of active participation strategy is as follows:

$$F(\mathbf{y}) = \frac{dy}{dt} = \begin{aligned} y(\mathcal{U}\_{21} - \mathcal{U}\_{2}) &= y(1-y) \left\{ \mathbf{x}[\mathcal{E}\_{1}(a\_{2}+c) + \mathcal{K}\_{1}a\_{1}(1-\beta\_{1})\lambda\_{2}\mathcal{K}\_{2}\theta\_{2} + z\_{2}c(a\_{1}\mathcal{K}\_{1})^{h}(a\_{2}\mathcal{K}\_{2})^{i} + \mathcal{K}\_{2}(1-\beta\_{2})\mathcal{K}\_{1}\theta\_{2} + \mathcal{K}\_{1}a\_{1}(1-\beta\_{1})\lambda\_{2}\mathcal{K}\_{2}\theta\_{2} + z\_{2}c(a\_{1}\mathcal{K}\_{1})^{h}(a\_{2}\mathcal{K}\_{2})^{h}(a\_{2}\mathcal{K}\_{2})^{h} + \mathcal{K}\_{2}(1-\beta\_{2})\mathcal{K}\_{1}\theta\_{2} + z(1-\beta\_{1})\mathcal{K}\_{1}\theta\_{2} + \mathcal{K}\_{2}a\_{1}(1-\beta\_{1})\mathcal{K}\_{2}\theta\_{2} \right\} \end{aligned}$$

In order to solve the equilibrium point-of-evolution game, let *<sup>F</sup>*(*x*) = 0 and *<sup>F</sup>*(*y*) = 0, five local equilibrium points can be obtained: a (0,0), B (0,1), C (1,0), D (1,1) and E (*x*<sup>∗</sup>, *y*<sup>∗</sup>). Where *<sup>x</sup>*<sup>∗</sup>,*y*∗ are:

$$\mathbf{x}^\* = \frac{K\_2(b\_2 + d\_2) \overset{\mathcal{I}}{+} m\_2 \overset{\mathcal{I}}{E}\_2 + \Delta K\_2 \lambda\_2 \theta\_2 - R\_{\xi 2} - G\_2 - K\_2(1 - \beta\_2)\gamma\_{21} - K\_2 \beta\_2 \gamma\_{22}}{E\_1(a\_2 + c) + K\_1 a\_1 (1 - \beta\_1)\lambda\_2 K\_2 \theta\_2 + z\_2 c \left(a\_1 K\_1\right)^h \left(a\_2 K\_2\right)^i + K\_2 (1 - \beta\_2) \xi - m\_2 a\_2 K\_2 - G\_2 + T}$$

$$y^\* = \frac{K\_1(b\_1 + d\_1) + m\_1 E\_1 + \Delta K\_1 \lambda\_1 \theta\_1 - R\_{\frac{\pi}{2}1} - K\_1(1 - \beta\_1)\gamma\_{11} - K\_1 \beta\_1 \gamma\_{12}}{E\_2 a\_1 + K\_2 a\_2 (1 - \beta\_2) \lambda\_1 K\_1 \theta\_1 + z\_1 c (a\_1 K\_1)^h (a\_2 K\_2)^i + K\_1 (1 - \beta\_1) \xi - n\_1 a\_1 K\_1 - G\_1 + F + T}$$

#### *4.3. Equilibrium Stability Strategy Analysis*

According to Hirshleifer theory [59], the Jacobian matrix can be used to analyze the local stability of the evolutionary system at the above five equilibrium points. According to the dynamic replication equation, the Jacobian matrix is obtained.

$$J = \begin{bmatrix} \frac{\partial F(\mathbf{x})}{\partial(\mathbf{x})} \frac{\partial F(\mathbf{x})}{\partial(\mathbf{y})} \\ \frac{\partial F(\mathbf{y})}{\partial(\mathbf{x})} \frac{\partial F(\mathbf{y})}{\partial(\mathbf{y})} \end{bmatrix} = \begin{bmatrix} AB \\ CD \end{bmatrix}$$

Among them,

 −

 −

$$\begin{cases} A &= (1 - 2\mathbf{x}) \left\{ y \big[ \mathbf{E}\_2 a\_1 + \mathbf{K}\_2 a\_2 (1 - \beta\_2) \lambda\_1 \mathbf{K}\_1 \theta\_1 + \mathbf{z}\_1 \mathbf{c} (\mathbf{a}\_1 \mathbf{K}\_1)^h (a\_2 \mathbf{K}\_2)^i + \mathbf{K}\_1 (1 - \beta\_1) \mathbf{J} \\ &- n\_1 a\_1 \mathbf{K}\_1 - \mathbf{G}\_1 + \mathbf{F} + \mathbf{T} \right] + \left[ \mathbf{R}\_{\frac{\beta\_1}{2}} - \mathbf{K}\_1 (\mathbf{b}\_1 + \mathbf{d}\_1) - m\_1 \mathbf{E}\_1 - \Delta \mathbf{K}\_1 \lambda\_1 \theta\_1 + \mathbf{K}\_1 (1 - \beta\_1) \gamma\_{11} + \mathbf{K}\_1 \beta\_1 \gamma\_{12} \right] \end{cases}$$

$$B = x(1-x)[E\_2a\_1 + K\_2a\_2(1-\beta\_2)\lambda\_1 K\_1\theta\_1 + z\_1c(a\_1K\_1)^h(a\_2K\_2)^i + K\_1(1-\beta\_1)\xi - n\_1a\_1K\_1 - G\_1 + F + T]$$

$$C = y(1-y)[E\_1(a\_2+c) + K\_1a\_1(1-\beta\_1)\lambda\_2 K\_2\theta\_2 + z\_2c(a\_1K\_1)^h(a\_2K\_2)^i + K\_2(1-\beta\_2)\xi - n\_2a\_2K\_2 - G\_2 + T]$$

$$D = \begin{array}{c} (1-2y)\left\{x[E\_1(a\_2+c) + K\_1a\_1(1-\beta\_1)\lambda\_2 K\_2\theta\_2 + z\_2c(a\_1K\_1)^h(a\_2K\_2)^i + K\_2(1-\beta\_2)\xi \\ -n\_2a\_2K\_2 - G\_2 + T] + [R\_{g2} + G\_2 - K\_2(b\_2 + d\_2) - m\_2E\_2 - \Delta K\_2\lambda\_2\theta\_2 + K\_2(1-\beta\_2)\gamma\_{21} + K\_2\beta\_2\gamma\_{22}]\right\} \end{array}$$

 −  −

 Then the trace of the matrix is: *trJ* = *A* + *D*.

The determinant of the Jacobian matrix and the sign of trace can determine when the above five equilibrium points are stable strategies (ESS). When *trJ* < 0 and det*J* = |*J*| > 0 are satisfied, the equilibrium point reaches a stable state and finally becomes a stable strategy. Because *<sup>x</sup>*<sup>∗</sup>, *y*∗ ∈ [0, 1], we ge<sup>t</sup>

 −

$$K\_1(b\_1 + d\_1) + m\_1 E\_1 + \Delta K\_1 \lambda\_1 \theta\_1 - R\_{\mathbb{S}^1} - K\_1 (1 - \beta\_1) \gamma\_{11} - K\_1 \beta\_1 \gamma\_{12} > 0$$

$$K\_2(b\_2 + d\_2) + m\_2 E\_2 + \Delta K\_2 \lambda\_2 \theta\_2 - R\_{\mathfrak{g}2} - G\_2 - K\_2 (1 - \beta\_2) \gamma\_{21} - K\_1 \beta\_1 \gamma\_{22} > 0$$

That is, when both sides choose to govern independently, the benefits are greater than those of one party seeking cooperation with the other. It shows that if the two sides cannot reach a cooperation agreement, the active participants will suffer a grea<sup>t</sup> loss. The overall benefit of the consistent direction peers or reverse peers is less than that of negative peers. Under this condition, the local stability results of the five equilibrium points are shown in Table 2.


**Table 2.** Local stability analysis of equilibrium point.

It can be seen from Table 2 that there are two unstable points B (0,1) and C (1,0) in the evolution system of green governance peer behavior of the focus governmen<sup>t</sup> and non-focus government. Point E (*x*<sup>∗</sup>, *y*<sup>∗</sup>) is the saddle point and point A (0,0) and point D (1,1) are the stable points of the system. Therefore, the evolution phase diagram of the system is shown in Figure 4.

**Figure 4.** Phase diagram of system evolution.

It can be seen from Figure 4 that the saddle point position determines the stable strategy and the final partner state of the focus governmen<sup>t</sup> and the non-focus government. Taking the broken line connected by points B, C, and E as the convergence critical line of the system, at the top right of the broken line (BECD) the system converges to the positive-peer state. In the lower left part of the broken line (ABEC part), the system converges to the negative-peer state. The larger the area of convergence region (BECD or ABEC), the closer the system is to the stable point (points D, A).

#### *4.4. Influence of Knowledge Management on the Evolution Trend of Peer Behavior* 4.4.1. The Evolution Trend of Peer Behavior in the Internalization Stage of ExternalKnowledge

From the expressions of *x*<sup>∗</sup> and *y*<sup>∗</sup>, we can see that:


Conclusion 1: The stronger the trust relationship between the two types of governments, the closer the exchange of managemen<sup>t</sup> will be, and the knowledge learning effect will promote the two sides to enter into a positive-peer state. The two types of governmen<sup>t</sup> should intensify the frequency of communication, actively align their willingness to green governance and strengthen the positive-peer effects.

Conclusion 2: In the process of knowledge synergy, if the two types of governmen<sup>t</sup> knowledge structure are complementary and the non-focus governmen<sup>t</sup> is willing to give part of the synergy benefits to the focus government, this will contribute to the stability of the positive-peer state of both sides. At this point, non-focal governments should focus on the long-term benefits of green governance and avoid short-term horizons that limit the positive-peer effects.

Conclusion 3: If the ability of knowledge cooperation and development is strong, it will obtain a higher knowledge reciprocity effect to maintain a positive-peer state. Therefore, the two types of governments should dovetail their spatial governance policies to jointly promote green industry development to avoid the excessive losses of a single development.

#### 4.4.2. Evolution Trend of Peer Behavior in Internal Knowledge Externalization Stage

From the expressions of *x*<sup>∗</sup> and *y*<sup>∗</sup>, we can see that:


Conclusion 4: The higher the cost of the tacit knowledge exchange between the two types of government, the weaker the knowledge learning effect acquired by both sides, which leads to a negative-peer state for both sides.

Conclusion 5: The higher degree of protection for the two types of governmen<sup>t</sup> will lead to higher value knowledge and the overcrowding of the knowledge transformation platform will lead to the closure of knowledge activities, which will make it difficult for both sides to obtain the knowledge spillover effect. This tends to lead to a negative-peer state.

4.4.3. Peer Behavior Evolution Trend in Internal Knowledge Transformation Stage

From the expressions of *x*<sup>∗</sup> and *y*<sup>∗</sup>, we can see that:

• The increment of autonomous governance knowledge Δ *K*1 and Δ *K*2 are positively correlated with *x*<sup>∗</sup> and *y*<sup>∗</sup>. With the increase of parameter value, the system converges to the negative-peer state. This shows that when the two players choose the selfgovernance strategy, the value-added benefits brought by self-focused development are higher than that of knowledge collaborative transformation, so they tend to choose the negative-peer state. There is no doubt that in this development mode,

both focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> can construct a green governance mode with local characteristics and expand the stock of governmen<sup>t</sup> knowledge. However, due to the weak foundation of non-focus government, the knowledge increment of the two is obviously not at the same level, which leads to the further widening of the development gap. This is also the 'negativity' of the negative-peer state. From the perspective of revenue, the knowledge incremental revenue of both sides is obviously greater than the knowledge synergy effect revenue in the short term. Because the latter needs continuous investment and stable knowledge exchange channels (low knowledge protection, low platform occupancy rate, etc.), the two types of governments tend to choose autonomous governance.

• The chance loss coefficient *γ*11, *γ*21 and knowledge protection penalty coefficient *γ*12, *γ*22 are negatively correlated with *<sup>x</sup>*<sup>∗</sup>, *y*<sup>∗</sup>. With the increase of the parameter value, the system converges to a positive-peer state. The higher the value of knowledge opportunity utilization and the greater the punishment to knowledge protection forces both sides to choose the actively lead and actively participate strategy. As a rational decision, when one party is idle or the redundant knowledge is too much, the other party needs corresponding knowledge to make up for it. The knowledge collaborative transformation activity can not only enlarge the value of knowledge, but also reduce punishment by opening knowledge and promoting the green collaborative development of the region.

Conclusion 6: The stronger the ability of the two kinds of governments to mine their own knowledge, the lower their willingness to participate in knowledge interaction, which leads to the formation of a negative-peer state.

Conclusion 7: The increase of opportunity and income of knowledge will enhance the willingness of the two types of governmen<sup>t</sup> to participate in knowledge interaction. The increase of knowledge protection punishment will further promote the formation of a positive-peer state.

#### 4.4.4. Influence of External Constraints of Knowledge Management on the Evolutionary Trend of Behavior of the Peer

From the expressions of *x*<sup>∗</sup> and *y*<sup>∗</sup>, we can see that the loss of credit *T* and punishment *F* are decreasing functions of *x*<sup>∗</sup> and *y*<sup>∗</sup>. When the value of *T* or *F* is increased, saddle point E tends to be stable point A. This shows that the greater the loss of governmen<sup>t</sup> image or reputation, the more the governmen<sup>t</sup> external expenditure caused by breach of contract and the resulting loss makes the organization tend to choose positive behavior. Considering that the central governmen<sup>t</sup> is not willing to lead the focus government, the greater the exit penalty of the focus governmen<sup>t</sup> is, the more the focus governmen<sup>t</sup> will choose to actively lead. Therefore, in the consistent direction peer, punishment *F* suppresses the formation of the consistent-direction-peer state, while reputation loss *T* promotes the non-focus governmen<sup>t</sup> to expand internal expenditure, avoid the occurrence of the adverse peer state, and finally guide both sides of the game to stabilize in the positive-peer state.

Conclusion 8: Stronger punishment and stronger binding forces of the intergovernmental cooperation contract will promote the two types of governments to maintain a positive-peer state.

#### *4.5. The Influence of Explicit and Tacit Knowledge Level on the Final Peer State*

In order to investigate the influence of explicit and tacit knowledge level of the focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> on knowledge transformation behavior and final peer state more intuitively, this paper used MATLAB to carry out numerical simulation. The initial parameter assignment is shown in Table 3, and the initial behavior probability was set as (0.5,0.5). In this regard, the initial data were modelled and selected from governmen<sup>t</sup> reports on the Yangtze River Economic Zone, and the corresponding indicators that could be drawn upon were transformed to the same order of magnitude. For example, K1 is the average number of green governance policies made public by the three focus governments of Jiangsu, Zhejiang, and Shanghai over the years, while K2 is the average number of green governance policies of non-focus governments such as Anhui. Other indicators were similarly compared to ensure the validity of the simulation.


**Table 3.** Initial parameter assignment.

The effect of the willingness level of green governance (tacit knowledge level) on peer status was analyzed. With other parameters unchanged, it can be seen from Figure 5 that:


knowledge gap increases significantly, the positive will of the focus governmen<sup>t</sup> and the non-focus governmen<sup>t</sup> will first increase slightly.

(**a**) E < 20

(**b**) E > 20

**Figure 5.** Evolution of the same peer state of both sides of the game when the tacit knowledge level changes.

The effect of knowledge stock (explicit knowledge level) of green governance on peer status was analyzed. With other parameters unchanged, it can be seen from Figure 6:

• In Figure 6a, (1) when the explicit knowledge level of focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> is low as a whole (*K* < 10), both sides eventually tend to be in a negativepeer state (0, 0). Among them, the willingness of non-focus governments to actively participate increases slightly at first and then decreases slowly. The focus government's willingness to actively lead continues to decline, and the decline rate gradually slows down. Similar to the mechanism of tacit knowledge, with the increase of knowledge, the focus government's willingness to lead decreases and increases rapidly, and the expansion of the knowledge gap also leads to the decline of leadership intention. However, the willingness of non-focus governmen<sup>t</sup> to participate in the process of change is different. When the knowledge gap is large, the willingness of non-focus

governmen<sup>t</sup> to participate in the process of change is low. (2) With the decrease of their explicit knowledge level, the willingness curve of active participation rises. However, when the knowledge gap expands, the role of the knowledge spillover effect on nonfocus governmen<sup>t</sup> is reduced, and it is difficult for non-focus governmen<sup>t</sup> with a weak foundation to obtain favorable resources and generate substantial benefits through the knowledge spillover effect. In the background there are external investments but as profits and the focus government's active will are not strong, the non-focus governmen<sup>t</sup> tends to finally move to autonomous governance mode. It can be seen that the knowledge gap limits the role of the knowledge spillover effect, leading to a negative-peer state of the system.

•In Figure 6b, (1) when the explicit knowledge level of the focus governmen<sup>t</sup> and non-focus governmen<sup>t</sup> is higher as a whole ( *K* > 20) or the explicit knowledge gap changes, the final state of both side changes. With the obvious increase of the explicit knowledge gap, the positive will of both sides continues to decrease, which is faster than that in Figure 6a. This reflects the existing problems of regional green development: In order to build better and faster in the green advantage industry and give play to the 'first mover' advantage, the focus governmen<sup>t</sup> will speed up the pace of independent development, leading to the widening gap of explicit knowledge, such as the managemen<sup>t</sup> experience of local governments among regions. (2) When both sides are in a state of a high level of explicit knowledge, the benefit of the knowledge spillover effect is significantly higher than that of external expenditure. At this time, although the focus governmen<sup>t</sup> undertakes more external investment due to the rise of the stock of non-focus governmen<sup>t</sup> knowledge, the focus governmen<sup>t</sup> can also accept part of the spillover knowledge and make up for its own shortcomings. The two sides present the collaborative situation of mutual benefits and a win-win relationship, forming a (1,1) positive-peer state.

(**a**) K < 20 

**Figure 6.** *Cont.*

**Figure 6.** Evolution of the same peer state of both sides of the game when the level of explicit knowledge changes.

#### **5. Conclusions and Suggestions**

Based on the improved SECI model, this paper constructs a dynamic evolutionary game model of local governmen<sup>t</sup> green governance peer behavior and further explains the mechanism of knowledge managemen<sup>t</sup> on local governmen<sup>t</sup> green governance peer behavior. It also considers the effects of knowledge learning, knowledge spillover, knowledge synergy, and knowledge reciprocity in the process of knowledge internal and external transformation. The results show that:


participate in the collaborative transformation of knowledge increases, but because the high willing side bears too much cost, the collaborative relationship may break down.

• The knowledge spillover effect plays an important role in the later stage of green governance. With the increase of the capacity gap, the knowledge acceptance and transformation of non-focus governmen<sup>t</sup> spillovers are limited, limiting the knowledge spillover effect. When peer interaction is positive, knowledge spillover will bring benefits.

Therefore, the following suggestions were put forward in this paper:


initiative to carry out knowledge spillover in the middle and later stages by following independently. Therefore, this paper encourages the formation of negative-peer, consistent-direction-peer, reverse-peer, and positive-peer development paths. All kinds of companion states are reasonable and necessary. The governmen<sup>t</sup> should rationally analyze the path of green governance decision-making to formulate appropriate development plans.

The article examines green governance in China from the perspectives of central and local governments, focus and non-focus governments, but the following shortcomings still exist: (1) The ultimate landing point of the government's green governance is still on the green innovative enterprises. The article only considers the impact of the peer effects among local governments on green governance, and subsequent studies can add the role of enterprises. (2) In terms of methodology, the article adopts a two-party evolutionary game approach. In subsequent studies, green innovation enterprises can be added to build a three-party evolutionary game model to analyze the government's green governance behavior more comprehensively.

**Author Contributions:** H.L. proposed the topic, designed the research content, and revised the final version of the paper. P.Y. participated in revising and editing the paper. X.W. and J.H. were involved in the simulation analysis and writing of the thesis. L.Y. provided guidance during the writing of the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Program of Shanghai Planning Office of Philosophy and Social Science of China (No. 2020BGL023).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
