Research on the Random Evolutionary Game of the Green Technology Innovation Alliance for Media Monitoring

Abstract

In the new media era, the green technology alliance with multi-participation has emerged as a powerful contributor to achieving the strategic goal of a green economy. Therefore, this paper constructs a stochastic evolutionary game model of green technology innovation led by the government under an uncertain environment and jointly promoted by enterprises, universities, and research institutes. Then, this study firstly explores the influence of different factors on evolutionary equilibrium and secondly discusses the role of main factors on the behavior strategies of each game subject. Furthermore, numerical simulation analysis using Matlab R2019a 9.6 will be used to prove the model’s validity. The research has shown (1) that media monitoring positively impacts the stability of the alliance and that product greenness can further accelerate alliance evolution when media monitoring is in place. When this factor is small, it will lead to the transformation of Industry-University-Research’s (IUR) optimal strategy into non-cooperation in the early stage. (2) The green degree of products positively affects the decision-making choice of the IUR, but it is not the case for the government. And the role of media supervision will further coordinate its influence and accelerate the evolution of alliances. (3) The enhancement of media monitoring capacity can encourage game subjects to evolve in a more beneficial way. In addition, the implementation of media supervision will help reduce the cost of government supervision and provide reputation benefits. The research fully accounts for the complexity and variability of the environment, and the results provide theoretical support and practical advice for the high-quality development of the green technology innovation alliance.

1. Introduction

Innovation and green are the main themes of the new development stage of countries worldwide. Incorporating the principles of green development into economic and social progress represents an effective strategy for accelerating the healthy, circular, and sustainable advancement of low-carbon countries. Countries are actively leveraging green technology innovation to expedite the attainment of “carbon peak” and “carbon neutrality” goals. This endeavor is aimed at further realizing the national strategic objective of promoting green economic development [1].

To this end, relevant guidance documents have been issued by Chinese government departments, clearly indicating that the government should integrate various resources and leverage the diverse functions of all stakeholders. Furthermore, the Chinese government has emphasized the necessity of accelerating the establishment of a green technology innovation alliance, with the government serving as a guiding force and enterprises, universities, and research institutes (UR) acting as primary participants [2].

As a new and efficient means to solve the problem of coordination between economic development and ecological environment [3], green technology innovation has a significant role in regulating and promoting artificial intelligence, green credit, and productive life [4,5,6]. As a novel and effective approach to addressing the coordination challenges between economic development and ecological environment [3], green technology innovation plays a significant role in regulating and advancing artificial intelligence, green credit systems, and sustainable production practices [4,5,6]. Many researchers agree that green technology innovation will make the sustainable economic growth and environment of the country better, and implementing the government’s circular economy policy has undoubtedly become one of the important factors of this result [7,8,9]. It is important to note that when governments adopt optimal green technology subsidies, the motivation of enterprises to optimize green technology investment and emission reduction increases [10]. With the advancement and application of evolutionary games, an increasing number of experts have recognized the study of evolutionary games of multi-party green technology innovation and applied it more extensively across various fields, including economics and daily life [11,12]. Some researchers have identified several key factors contributing to the fragmentation of industry-university-research (IUR) alliances. These include the stability of trust between partners, government green subsidies provided to various stakeholders, the investment benefits for enterprises, the variability in managerial behavior and decision-making processes, as well as the consumption costs incurred by consumers [13,14,15]. In addition, several scholars have analyzed longitudinally how university-industry alliances or inter-enterprise alliances influence the decisions of key subjects through benefit and trust games [16,17,18,19]. These analyses sufficiently reflect the current societal objective of green economic development, which aims to leverage green technology innovation for multidisciplinary applications. Furthermore, it underscores the cooperative strategies in green technology innovation adopted by various parties to collectively stimulate the national green economy.

With the application of evolutionary game theory, the current literature has developed and analyzed multi-party evolutionary game models across various scenarios. Concurrently, studies have also examined the stability of the IUR alliance [20] and explored green technology innovation [21]. All of these achievements have established the ideological foundation for this study. However, in the context of a highly uncertain and complex reality, the importance of media monitoring capabilities cannot be overlooked. Existing research on the IUR green technology innovation alliance often focuses solely on analyzing specific influencing factors or individual game subjects, which significantly limits its ability to remain relevant in contemporary discussions. An in-depth study of the impact of media monitoring capacity on participant behavior, as well as the key factors that disrupt the stability of green technology innovation alliances in uncertain environments, can enhance existing game models derived from prior research. This improvement may lead to reduced government costs, increased reputational benefits for each participant, and greater stability in alliance cooperation, ultimately contributing to the development of a global green economy. Simultaneously, this study reinforces the theoretical foundation for subsequent research on multi-party green technology innovation alliances. It offers a more reliable reference value for decision-making among all participants involved in these games.

Therefore, to further analyze the undertakings of IUR events in an uncertain environment, this paper develops a multi-party stochastic evolutionary game model for the government-industry-university-research (GIUR) collaboration based on the aforementioned research analysis. The model integrates four key variables: the degree of stochastic interference, media monitoring capacity, government incentives, and product greenness, and treats their influence degrees as continuous variables transitioning from almost non-action to almost complete action and further imports Gaussian stochastic interference terms. Building upon this framework, we analyze and explore the entire evolving alliance system. The stable equilibrium solution of the solved model is proved. Numerical simulations are carried out, and the sensitivity of the change in the parameters’ values to the systematic stability is investigated with the simulation results. The corresponding results and targeted optimization suggestions are given.

In summary, the primary contributions of this paper are as follows: (1) Considering the uncertainty of the world, we introduce a random interference system into the strategic analysis of alliances and construct a multi-party random evolution game model focused on green technology innovation within the GIUR framework. (2) By employing random evolution game theory, we derive stability conditions for tripartite game strategies operating under a random interference environment. (3) We incorporate media monitoring capabilities into the GIUR alliance and conduct a detailed numerical simulation to analyze how this factor influences both the stability of green technology innovation alliances and other relevant factors.

2. Literature Review

2.1. Game Model of GIUR

In the late 20th century, scholars Henry Etzkowitz and Loet Leydesdorff introduced the role of government into the game model. They proposed the interactive relationship theory of GIUR, which elucidates a novel type of interaction among three key parties in the evolution of economic unions—the “triple helix” [22,23]. Senker [24] posits that highly diffuse and spillover scientific research projects are generally inseparable from government support and emphasizes that government leadership and support are crucial to the IUR alliance. Chen et al. [25] observed the government’s tax reduction and subsidy policies are conducive to optimizing enterprises’ green production modes, thereby confirming that governmental support effectively promotes the country’s green production and sustainable living practices [26,27]. Wu et al. [28] conducted empirical research and found that government policies exert a significant stimulating effect on green technology innovation. Furthermore, the quantity and effectiveness of these policies directly influence the output of enterprises’ green technology innovations. Subsequently, scholars Sotarauta and Suvinen [29] examined the diverse roles of green technology innovation consortia within the ecosystem. They conducted an analysis of the significant alliances formed through GIUR cooperation, which are crucial for advancing pioneering innovations in clean technology. Chen et al. [30] incorporated the government as a participant in their study of the Green Technology Innovation Alliance. They included the hypothesis of greenness variables, filling the gap that existing literature had not paid much attention to government participants and technology innovation in the GIUR. However, they did not account for the impact of media monitoring capacity on participants’ strategic choices within the GIUR alliance focused on green technology innovation in a heterogeneous society.

2.2. The Impact of Media Monitoring

Media, as the fourth estate independent of the three primary political powers in today’s Internet society, exerts an increasingly significant economic impact on social activities. This influence is amplified by its role as a hub for information circulation and thus cannot be underestimated. Besley and Prat [31], as well as Li et al. [32], have examined the economic effects of media on market dynamics. They highlighted that media reports primarily rely on reputation constraints and public opinion pressure to effectively regulate the behavioral decisions of various stakeholders within competitive environments. Through relevant data, Chen et al. [33] demonstrate that regional digitization and environmental governance have enhanced the media effectiveness of green innovation. They find that positive media coverage serves to promote advancements in green innovation. Zhang et al. [34] investigate a model of government contractors characterized by interactive relationships grounded in bounded rationality. The findings indicate that while there are stringent sanctions imposed on contractors who fail to engage in ecological construction, the system can effectively regulate the availability of advertisements or the exposure capacity of media, thereby establishing a stable strategy. Based on an assessment of the COVID-19 pandemic, Han et al. [35] investigated the impact of media exposure on public assessment. They proposed that enhancing the relationship between media trust and perceptions of media bias could foster positive social developments. Zhou et al. [36] highlighted that winning media generates stronger impulse buying intentions compared to owned media. Oliver et al. [37] examined and concluded that, in the context of income related to reputation and other pertinent influencing factors, media hold significant social importance and tangible value benefits for stakeholders. Furthermore, media monitoring serves as a complement to governmental oversight, reducing costs while enhancing the reputational benefits for each participant in various sectors, thereby reinforcing alliance stability. However, there is a notable scarcity of literature addressing how media monitoring influences the evolutionary stability of Green Technology Innovation Alliances.

3. Methods and Analysis

3.1. Problem Description and Model Construction

Transaction cost theory finds that, although the IUR collaboration has great advantages in technology research and development, resource utilization, and cooperation costs [38,39,40], it also has high cooperation expenditure, mainly in finding partners, collaborative communication, and intellectual property protection [41]. However, the existing IUR green technology innovation alliance failed to adapt to the market environment with strong interference and high uncertainty. Government intervention can compensate for market failures by improving the complex and volatile internal and external environment induced by technical complexity or public opinion through legal, policy, and other means [25], further increasing the willingness of game parties to cooperate, maintaining the long-term stability of the alliance, and stimulating market activity.

And in recent years, many experts and scholars have noted the importance of media participation or media monitoring. The study revealed that media monitoring positively influences reputation income [42], enhances emergency management capabilities [43], and improves the quality of tourism [44]. To better study game research in uncertain environments, experts and scholars realized that it was necessary to find a factor to express the random disturbance of the system, so they combined the theory of random analysis [45,46] and game theory [47,48] to introduce Gaussian white noise. In addition, the stability boundary conditions of dynamic equations based on random replicators are given in the literature [49,50].

Therefore, in light of the uncertain external market conditions and the bounded rationality inherent in alliances, research on green technology innovation alliances formed by enterprises and research institutions is insufficient to effectively navigate the complexities of both internal and external environments. This study, according to the stakeholder theory [51], the main stakeholders involved in the GIUR green technology innovation alliance are government, industry, and academic research institutions. In view of this, the basic assumptions of the model are as follows:

Assumption 1.

The participants in the game—namely; the government; industry; and the UR—are all finite rational agents.

Assumption 2.

The government’s strategy is (regulate, not regulate). The government’s regulation cost is $C_0$, and the benefits to the government of choosing to regulate is $S_1$, and choosing not to regulate is $S_2$, where $S_1>S_2>0$.

Assumption 3.

The government will implement specific incentives for enterprises and the UR in order to encourage the growth of the national economy. The government incentives to enterprises is $K_1$, and the incentives to the UR is $K_2$. The government incentives for enterprises to choose to cooperate is $\alpha$, and the government incentives for the UR to choose to cooperate is $\beta$, where $\alpha \in (0, 1),\beta \in (0, 1)$.

Assumption 4.

The enterprises’ strategy is to (cooperate, midway betrayal). The enterprise’s initial investment cost is $C_1$, and its subsequent cost of remaining in the partnership is $C_3$. The proportion of the initial cost of continuing to cooperate that the enterprise chooses to betray is ${\gamma }_1$, where ${\gamma }_1\in (0, 1)$, then the subsequent cost of betrayal is ${\gamma }_1{C}_3$. The benefit gained by the enterprise before it chooses not to cooperate is $L_1$, and the benefits that enterprises gain from the value of the technologies learned during the cooperation period is $L_3$.

Assumption 5.

The strategy of the UR is (active R&D and midway betrayal). The URs initial investment cost is $C_2$, and the subsequent cost of continuing to participate in the collaboration is $C_4$. The proportion of the initial cost of continuing active R&D that the UR chooses to midway betray is ${\gamma }_2$, where ${\gamma }_2\in (0, 1)$, then the subsequent cost of betrayal is ${\gamma }_2{C}_4$. The benefit of the UR before to deciding not to cooperate is represented by the $L_2$, and the value income or financial support of the semi-finished products acquired during the cooperation time is represented by the $L_4$.

Assumption 6.

Under governmental oversight, the subject who chooses to betray midway should compensate $P$to the betrayed subject. ${\phi }_i$ represents the value-benefit ratio of harvest that the subject who chooses to cooperate receives from the subject who betrays midway, where ${\phi }_i\in \left(0, 1\right), i=1, 2$. As an illustration, ${\phi }_1$ shows the equivalent value of the knowledge, technology, and ideas learned by the industry from the beginning to the betrayal of the UR. ${\phi }_2$indicates the equivalent value of the semi-finished product or inspiration acquired by the UR from the beginning to the time of the betrayal by the industry.

Assumption 7.

The total green innovation value added by the enterprise and the UR, choosing to continue the collaboration, is $\Delta \pi$. Assuming that the percentage of value-added green innovation by enterprises is $\theta$, then, the percentage of the UR is $1-\theta$, where $\theta \in (0, 1)$, and $\epsilon$ is the greenness of the products produced in collaboration?

Assumption 8.

Media monitoring is added to reduce the government’s regulatory burden. The monitoring capacity of the media is $\varphi$, where $\varphi \in (0, 1)$. Regarding the reputation gains obtained by the game subjects, the government gains $R_1$ when it chooses to regulate, the firm gains $R_2$ when it chooses to cooperate, and the UR gains when it chooses to actively research and develop $R_3$.

Assumption 9.

For the government, the probability of choosing supervision and non-supervision is $x(0<x<1)$ and $1-x$, respectively. For enterprises, the probability of choosing cooperation and betrayal in the middle is $y(0<y<1)$ and $1-y$, respectively. For the UR, the probability that it chooses active R&D and midway betrayal is $z(0<z<1)$ and $1-z$, respectively.

The payment matrix for the evolutionary game between the government, industry, and the UR parties is created as shown in

Table 1. Payoff matrix.

Strategy Selection				Academia and Research Parties
				Actively Research and Develop (z)	Betray in the Middle (1 − z)
Government	Supervise ($x$)	Companies	Cooperate ($y$)	$S_1-\left(1-\mathsf{\phi }\right)C_0+\phi R_1+\alpha K_1-\beta K_2$ $L_1+\epsilon \theta \Delta \pi -C_1-C_3+\phi R_2+\alpha K_1$ $L_2+\epsilon \left(1-\theta \right)\mathsf{\Delta }\pi -C_2-C_4+\phi R_3+\beta K_2$	$S_1-\left(1-\phi \right)C_0+\phi R_1-\alpha K_1$ $L_1-C_1-C_3+\phi R_2+\alpha K_1+P+{\varphi }_1{L}_4$ $L_2+L_4-C_2-{\gamma }_2{C}_4-P$
			Midway betray ($1-y$)	$S_1-\left(1-\phi \right)C_0+\phi R_1-\beta K_2$ $L_1+L_3-C_1-{\gamma }_1{C}_3-P$ $L_2-C_2-C_4+\phi R_3+\beta K_2+P+{\varphi }_2{L}_3$	$S_1-\left(1-\phi \right)C_0+\phi R_1$ $L_1+L_3-C_1-{\gamma }_1{C}_3$ $L_2+L_4-C_2-{\gamma }_2{C}_4$
	not Supervise (1$-x$)	Companies	Cooperate ($y$)	$S_2$ $L_1+\epsilon \theta \mathsf{\Delta }\pi -C_1-C_3+\phi R_2$ $L_2+\epsilon \left(1-\theta \right)\mathsf{\Delta }\pi -C_2-C_4+\varphi R_3$	$S_2$ $L_1-C_1-C_3+\phi R_2+{\varphi }_1{L}_4$ $L_2+L_4-C_2-{\gamma }_2{C}_4$
			Midway betray ($1-y$)	$S_2$ $L_1+L_3-C_1-{\gamma }_1{C}_3$ $L_2-C_2-C_4+\phi R_3+{\varphi }_2{L}_3$	$S_2$ $L_1+L_3-C_1-{\gamma }_1{C}_3$ $L_2+L_4-C_2-{\gamma }_2{C}_4$

Note: Each of the aforementioned variables is greater than or equal to 0.

based on the aforementioned parameter hypotheses. The meanings of the symbols are shown in

Table 2. The table of symbols.

Parameter	Meanings	Parameter	Meanings
${\mathrm{C}}_0$	The government’s regulation cost	${\mathrm{L}}_1$	The benefit gained by the enterprise before it chooses not to cooperate
${\mathrm{C}}_1$	The enterprises’ initial investment cost	${\mathrm{L}}_2$	The income of the UR before deciding not to cooperate
${\mathrm{C}}_2$	The URs initial investment cost	${\mathrm{L}}_3$	The benefits that enterprises gain from the value of the technologies learned during the cooperation period.
${\mathrm{C}}_3$	The enterprises’ subsequent cost of remaining in the partnership	${\mathrm{L}}_4$	The value of income or financial support of the semi-finished products acquired during the cooperation time of the UR
${\mathrm{C}}_4$	The URs subsequent cost of continuing to participate in the collaboration	$\mathrm{P}$	Compensation given by the subject who betrays the betrayed subject.
${\mathrm{S}}_1$	The benefits to the government of choosing to regulate	$\mathsf{\phi }$	The value-benefit ratio of harvest that the subject that chooses to cooperate receives from the subject that midway betrayal
${\mathrm{S}}_2$	The benefits to the government of choosing not to regulate	$\mathsf{\Delta }\mathsf{\pi }$	The total green innovation value added by the enterprise and the UR, choosing to continue the collaboration
${\mathrm{K}}_1$	The government incentives to enterprises	$\mathsf{\theta }$	The percentage of value-added green innovation by enterprises
${\mathrm{K}}_2$	The government incentives to the UR	$1-\mathsf{\theta }$	The percentage of value-added green innovation by UR
$\mathsf{\alpha }$	The government incentives for enterprises to choose to cooperate	$\mathit{\varphi }$	The monitoring capacity of the media
$\mathsf{\beta }$	The government incentives for the UR to choose to cooperate	${\mathrm{R}}_1$	The reputational benefits of government choosing to regulate
${\mathsf{\gamma }}_1$	The proportion of the initial cost of continuing to cooperate that the enterprise chooses to betray	${\mathrm{R}}_2$	The reputational benefits of enterprises choosing to cooperate
${\mathsf{\gamma }}_2$	The proportion of the initial cost of continuing active R&D that the UR chooses to midway betray	${\mathrm{R}}_3$	The reputation benefits of active research and development by the UR
$\mathsf{\epsilon }$	The greenness of the products produced in collaboration

.

3.2. Stochastic Evolutionary Game Model

3.2.1. The Replication Dynamic Equations

The predicted payoffs and replication dynamic equations for the selection of strategies by the government, enterprises, and the UR, respectively, may be obtained using the payoff matrix in Table 1.

Assuming that the benefits of the government’s choice to “regulate” is $U_1$, and “not regulate” is $U_2$. Its average benefit is $\bar{U}$, then,

$$U_1=\left(C_0+R_1\right)\mathit{\phi }-K_1\alpha y-K_2\beta z+S_1-C_0$$

(1)

$$U_2=S_2$$

(2)

$$\bar{U}=x{U}_1+(1-x)U_2=\left(\right(C_0+R_1)\phi -K_1\alpha y-K_2\beta z-C_0+S_1-S_2)x+S_2$$

(3)

Coupling Equations (1) and (3) yields the replication dynamics equation for the government as follows.

$$F(x)={\displaystyle \frac{dx}{dt}}=x(U_1-\bar{U})=x(1-x)(U_1-U_2)=x(1-x)((C_0+R_1)\phi -K_1\alpha y-K_2\beta z-C_0+S_1-S_2)$$

(4)

Assuming that the benefits of the firm’s choice of “cooperation” is $V_1$, and to “betrayal in the middle” is $V_2$. Its average benefit is $\bar{V}$, then,

$$V_1=(\alpha K_1-Pz+P)x+(\epsilon \theta \Delta \pi -{\varphi }_1{L}_4)z+{\varphi }_1{L}_4+\phi R_2-C_1-C_3+L_1$$

(5)

$$V_2=-Pxz-{\gamma }_1{C}_3-C_1+L_1+L_3$$

(6)

$$\bar{V}=y{V}_1+(1-y)V_2=\left(\right({\gamma }_1-1)C_3+(\alpha K_1+P)x+(\epsilon \theta \Delta \pi -{\varphi }_1{L}_4)z+{\varphi }_1{L}_4+\phi R_2-L_3)y-Pxz-{\gamma }_1{C}_3-C_1+L_1+L_3$$

(7)

Coupling Equations (5) and (7) yields the replication dynamics equation for the firm as follows.

$$F(y)={\displaystyle \frac{dy}{dt}}=y(V_1-\bar{V})=y(1-y)(V_1-V_2)=y(1-y)({\varphi }_1{L}_4(1-z)+({\gamma }_1-1)C_3+(\alpha K_1+P)x+\epsilon \theta \Delta \pi z+\phi R_2-L_3)$$

(8)

Assuming that the benefits of “active R&D” is $W_1$, and that the average benefit is $W_2$. Its average benefit is $\bar{W}$, then,

$$W_1=(-Px+\epsilon (1-\theta )\Delta \pi -{\varphi }_2{L}_3)y+(\beta K_2+P)x+{\varphi }_2{L}_3+\phi R_3-C_2-C_4+L_2$$

(9)

$$W_2=-Pxy-{\gamma }_2{C}_4-C_2+L_2+L_4$$

(10)

$$\bar{W}=z{W}_1+(1-z)W_2=\left(\epsilon \right(1-\theta )\Delta \pi -{\varphi }_2{L}_3)y+({\gamma }_2-1)C_4+(\beta K_2+P)x+{\varphi }_2{L}_3+\phi R_3-L_4)z-Pxy-{\gamma }_2{C}_4+L_4-C_2-C_4+L_2$$

(11)

Coupling Equations (9) and (11) yields the replication dynamic equation for the learned UR as follows.

$$\begin{gathered} F\left(z\right)={\displaystyle \frac{dz}{dt}}=z\left(W_1-\bar{W}\right)=z\left(1-z\right)\left(W_1-W_2\right)=z\left(1-z\right)((\epsilon \left(1-\theta \right)\Delta \pi \\ -{\varphi }_2{L}_3)y+\left({\gamma }_2-1\right)C_4+\left(\beta K_2+P\right)x+\phi R_3+{\varphi }_2{L}_3-L_4) \end{gathered}$$

(12)

3.2.2. Evolution Replication Dynamic Equation Under Random Disturbance

The degree of uncertainty in the world will have some bearing on the coalition members’ choice of strategy because it is a living and changing organism. Here, a matching stochastic evolutionary game model is developed using stochastic analysis theory, and under media scrutiny, the substantive impact of uncertainties on the government, industry, and UR is then explored [45]. According to the derivation results in Table 1 and Section 3.2.1, the replication dynamic equations for government, industry, and UR are as follows:

$$dx\left(t\right)=x\left(t\right)\left(1-x\left(t\right)\right)\left[\left(\left(C_0+R_1\right)\phi -K_1\alpha y-K_2\beta z-C_0+S_1-S_2\right)\right]dt+\sigma x\left(t\right)d\omega \left(t\right)$$

(13)

$$dy\left(t\right)=y\left(t\right)\left(1-y\left(t\right)\right)\left[\left({\varphi }_1{L}_4\left(1-z\right)+\left({\gamma }_1-1\right)C_3+\left(\alpha K_1+P\right)x+\epsilon \theta \Delta \pi z+\varphi R_2-L_3\right)\right]dt+\sigma y\left(t\right)d\omega \left(t\right)$$

(14)

$$dz\left(t\right)=z\left(t\right)\left(1-z\left(t\right)\right)\left[\left(\left(\epsilon \left(1-\theta \right)\Delta \pi -{\phi }_2{L}_3\right)y+\left({\gamma }_2-1\right)C_4+\left(\beta K_2+P\right)x+\phi R_3+{\varphi }_2{L}_3-L_4\right)\right]dt+\sigma z\left(t\right)d\omega \left(t\right)$$

(15)

where $\sigma$ is a random disturbance term, $\sigma =0$ indicates that the model has no random perturbation factor, and $\sigma =1$ indicates that the model has a random perturbation factor. $N\left(0,\sqrt{h}\right)\omega \left(t\right)$ is a one-dimensional standard Brownian motion, $d\omega \left(t\right)$ denotes Gaussian white noise, and when $t>0$, the step size $h>0$, and its increment $\Delta \omega \left(t\right)=\omega \left(t+h\right)-\omega \left(t\right)$ obeys the normal distribution [45].

Equations (13)–(15) are one-dimensional $It\widehat{o}$ stochastic differential equations containing Gaussian random disturbance terms. Represents the evolution replication dynamic equation of government, enterprise, and UR under random disturbance.

3.2.3. Analysis of the Existence and Stability of Equilibrium Solutions

According to Equations (13)–(15), let $t=0$, the initial moment of the game subject have $x\left(0\right)=0,y\left(0\right)=0,z\left(0\right)=0$, then,

$$0\times 1\times \left(\left(C_0+R_1\right)\phi -K_1\alpha y-K_2\beta z-C_0+S_1-S_2\right)+\sigma d\omega \left(t\right)\times 0=0$$

(16)

$$0\times 1\times \left({\varphi }_1{L}_4\left(1-z\right)+\left({\gamma }_1-1\right)C_3+\left(\alpha K_1+P\right)x+\epsilon \theta \Delta \pi z+\phi R_2-L_3\right)+\sigma d\omega \left(t\right)\times 0=0$$

(17)

$$0\times 1\times \left(\left(\epsilon \left(1-\theta \right)\Delta \pi -{\varphi }_2{L}_3\right)y+\left({\gamma }_2-1\right)C_4+\left(\beta K_2+P\right)x+\phi R_3+{\varphi }_2{L}_3-L_4\right)+\sigma d\omega \left(t\right)\times 0=0$$

(18)

From Equations (16) to (18), it can be seen that there is at least a zero solution to the equation ${\left.d\omega \left(t\right)\right|}_{t=0}={\left.{\omega }^{\prime }\left(t\right)dt\right|}_{t=0}=0$, i.e., when $\sigma =0$, the system will continuously maintain the state, so the zero solution is the equation’s equilibrium solution.

But in fact, the internal and external environments are inevitably going to destabilize the alliance, which has an impact on its long-term stability. Given this, stochastic elements must be taken into account when examining the durability of coalitions between the government, industry, and the UR. The stability criterion of the tripartite evolution game equation can be determined according to the stability criterion of stochastic differential equations. The stability criterion is as follows:

Lemma 1.

Let the stochastic differential equation $x=x\left(t\right),t\ge 0$ satisfy the solution of the initial value problem of the differential equation $It\widehat{o}$ [46]:

$$dx\left(t\right)=f\left(t,x\left(t\right)\right)dt+g\left(t,x\left(t\right)\right)d\omega \left(t\right),\forall t\ge 0,x\left(t_0\right)=x_0$$

(19)

Suppose there exist continuous differentiable functions $V\left(t,x\right)$ and positive constants $c_1,c_2$ makes $c_1{\left|x\right|}^p<V\left(t,x\right)<c_2{\left|x\right|}^p$.

Condition 1.

If there exists a positive constant $\gamma$, such that $LV\left(t,x\right)\le -\gamma V\left(t,x\right),t\ge 0$, then the zero solution of Equation (13) is exponentially stable in $p$ order moments and holds $E{\left|x\left(t,x_0\right)\right|}^p<\left(c_2/c_1\right){\left|x_0\right|}^p{e}^{-\gamma t},t\ge 0$

Condition 2.

If there exists a positive constant $\gamma$ such that $LV\left(t,x\right)\ge -\gamma V\left(t,x\right),t\ge 0$, then the zero solution of Equation (13) is exponentially unstable in $p$ order moments and holds $E{\left|x\left(t,x_0\right)\right|}^p\ge \left(c_2/c_1\right){\left|x_0\right|}^p{e}^{\gamma t},t\ge 0$, where $LV\left(t,x\right)=V_t\left(t,x\right)+V_x\left(t,x\right)f\left(t,x\right)+{\displaystyle \frac{1}{2}}{g}^2\left(t,x\right)V_{xx}\left(t,x\right)$

For Equations (13)–(15), take $V_t\left(t,x\right)=x,V_t\left(t,y\right)=y,V_t\left(t,z\right)=z,x\in \left[0,1\right],y\in \left[0,1\left],z\in \right[0,1\right],c_1=c_2=1,p=1,\gamma =1$, then:

$$LV\left(t,x\right)=f\left(t,x\right)=x\left(1-x\right)\left(\left(C_0+R_1\right)\phi -K_1\alpha y-K_2\beta z-C_0+S_1-S_2\right)$$

(20)

$$\begin{gathered} LV\left(t,y\right)=f\left(t,y\right)=y\left(1-y\right)({\varphi }_1{L}_4\left(1-z\right)+\left({\gamma }_1-1\right)C_3+\left(\alpha K_1+P\right)x \\ +\epsilon \theta \Delta \pi z+\phi R_2-L_3) \end{gathered}$$

(21)

$$\begin{gathered} LV\left(t,z\right)=f\left(t,z\right)=z\left(1-z\right)(\left(\epsilon \left(1-\theta \right)\Delta \pi -{\varphi }_2{L}_3\right)y+\left({\gamma }_2-1\right)C_4+ \\ \left(\beta K_2+P\right)x+\phi R_3+{\varphi }_2{L}_3-L_4) \end{gathered}$$

(22)

If the zero solution moment exponent of Equations (13)–(15) is stable, it needs to satisfy

$$x\left(1-x\right)\left(\left(C_0+R_1\right)\phi -K_1\alpha y-K_2\beta z-C_0+S_1-S_2\right)\le -x$$

(23)

$$\begin{gathered} y\left(1-y\right)\left({\varphi }_1{L}_4\left(1-z\right)+\left({\gamma }_1-1\right)C_3+\left(\alpha K_1+P\right)x+\epsilon \theta \Delta \pi z+\phi R_2-L_3\right) \\ \le -y \end{gathered}$$

(24)

$$\begin{gathered} z\left(1-z\right)(\left(\epsilon \left(1-\theta \right)\Delta \pi -{\varphi }_2{L}_3\right)y+\left({\gamma }_2-1\right)C_4+\left(\beta K_2+P\right)x+\phi R_3+ \\ {\varphi }_2{L}_3-L_4)\le -z \end{gathered}$$

(25)

After corresponding reduction and calculation of the above formula, the condition to satisfy Equation (23) is

${\mathrm{X}}_1$: When $y\in \left[0, 1\left],z\in \right[0, 1\right]$ and $\alpha K_1\ge 0$, $y\le {\displaystyle \frac{\left(\left(K_2\beta z+\left(1-\phi \right)C_0-\phi R_1+S_2-S_1\right)\left(1-x\right)-1\right)}{\alpha K_1\left(1-x\right)}}$

The conditions for Equation (24) are

${\mathrm{Y}}_1$: When $x\in \left[0,1\left],z\in \right[0,1\right]$ and $\epsilon \theta \Delta \pi -{\phi }_1{L}_4\ge 0$, $z\ge {\displaystyle \frac{-{\varphi }_1{L}_4+\left(1-{\gamma }_1\right)C_3-\left(\alpha K_1+P\right)x-\phi R_2+L_3-1}{\epsilon \theta \Delta \pi -{\varphi }_1{L}_4}}$;

${\mathrm{Y}}_2$: When $x\in \left[0,1\left],z\in \right[0,1\right]$ and $\epsilon \theta \Delta \pi -{\varphi }_1{L}_4\le 0$, $z\ge {\displaystyle \frac{-{\varphi }_1{L}_4+\left(1-{\gamma }_1\right)C_3-\left(\alpha K_1+P\right)x-\phi R_2+L_3-1}{\epsilon \theta \Delta \pi -{\varphi }_1{L}_4}}$

The conditions for Equation (25) are

${\mathrm{Z}}_1$: When $x\in \left[0,1\left],y\in \right[0,1\right]$, $\beta K_2+P\ge 0$ and $-\left(\epsilon \left(1-\theta \right)\Delta \pi -{\varphi }_2{L}_3\right)\le 0$, $x\le {\displaystyle \frac{-\left(\epsilon \left(1-\theta \right)\Delta \pi -{\varphi }_2{L}_3\right)y+\left(1-{\gamma }_2\right)C_4-\phi R_3-{\varphi }_2{L}_3+L_4-1}{\beta K_2+P}}$

${\mathrm{Z}}_2$: When $x\in \left[0,1\left],y\in \right[0,1\right]$, $\beta K_2+P\ge 0$ and $-\left(\epsilon \left(1-\theta \right)\Delta \pi -{\varphi }_2{L}_3\right)\ge 0$, $x\le {\displaystyle \frac{-\left(\epsilon \left(1-\theta \right)\Delta \pi -{\varphi }_2{L}_3\right)y+\left(1-{\gamma }_2\right)C_4-\phi R_3-{\varphi }_2{L}_3+L_4-1}{\beta K_2+P}}$

In conclusion, when ${\mathrm{X}}_1\cap ({\mathrm{Y}}_1\cap {\mathrm{Y}}_2)\cap ({\mathrm{Z}}_1\cap {\mathrm{Z}}_2)\ne \varnothing$, the zero-order moment index of Equations (23)–(25) are stable.

4. Results

This section provides simulation plots using Matlab 2019a to analyze and discuss the relevant parameters’ impact on the game subjects’ strategy choice, as well as to discuss the related issues. The analysis focuses on the effects of stochastic interference intensity $\sigma$, product greenness $\epsilon$, media monitoring capacity $\phi$, and government incentives $\alpha$ and $\beta$ on the stochastic evolution process of the government, industry, and UR parties, as well as exploring whether media monitoring capacity can accelerate product greenness and government incentives. The existing literature on related topics is usually based on real research data or expert scoring to value and verify these parameters [20,52,53,54], so this study is based on the parameter values of existing literature; the relevant variables take the following values (in millions): $S_1=23$, $S_2=12$, $C_0=5$, $C_1=5$, $C_2=5$, $C_3=8$, $C_4=5$, ${\gamma }_1=0.5$, ${\gamma }_2=0.5$, $\varphi =0.5$, $P=8$, $L_3=8$, $L_4=10$, $\Delta \pi =20$, $\theta =0.5$, $\epsilon =0.5$, ${\phi }_1=0.2$, ${\phi }_1=0.2$, $K_1=10$, $K_2=10$, $\alpha =0.5$, $\beta =0.6$, As a practical matter, the government lays more emphasis on reputation gain, the UR is second, and the enterprises pay more attention to the economic gain, i.e., $R_1=10$, $R_2=6$, $R_3=8$. The evolutionary initial states are $x=0.5$, $y=0.5$, $z=0.5$, and the step size $h=0.01$.

According to the Milstein higher-order method [55], the discretization equation is obtained as

$$x(t+1)=x(t)+x(t)(1-x(t))[((C_0+R_1)\phi -K_1\alpha y-K_2\beta z-C_0+S_1-S_2)]\Delta t+\sigma x(t)\sqrt{\Delta t}\xi +{\displaystyle \frac{1}{2}}{\sigma }^{2}x(t)({\xi }^2-1)\Delta t$$

(26)

$$y(t+1)=y(t)+y(t)(1-y(t))[({\phi }_1{L}_4(1-z)+({\gamma }_1-1)C_3+(\alpha K_1+P)x+\epsilon \theta \Delta \pi z+\phi R_2-L_3)]\Delta t+\sigma y(t)\sqrt{\Delta t}\xi +{\displaystyle \frac{1}{2}}{\sigma }^{2}x(t)({\xi }^2-1)\Delta t$$

(27)

$$z(t+1)=z(t)+z(t)(1-z(t))[((\epsilon (1-\theta )\Delta \pi -{\varphi }_2{L}_3)y+({\gamma }_2-1)C_4+(\beta K_2+P)x+\phi R_3+{\varphi }_2{L}_3-L_4)]\Delta t+\sigma z(t)\sqrt{\Delta t}\xi +{\displaystyle \frac{1}{2}}x(t)({\xi }^2-1)\Delta t$$

(28)

4.1. The Influence of Random Disturbance Intensity on the Evolutionary Process

This section mainly explores random disturbance intensity’s impact on the behavioral strategies of game subjects. Based on the Milstein higher-order method, we change the random disturbance intensity $\sigma$ ($\sigma =0.1, 0.5, 0.9$) in Equations (13)–(15), keep the rest of the parameters unchanged, and mimic the process through which the three parties—government; industry; and the UR—evolve their strategies as shown in Figure 1.

Figure 1 shows that when the interference intensity is very low ($\sigma =0.1$), the GIUR progressively evolves to a stable condition (see Appendix A for details). The game respondents typically stabilize their strategy more slowly as the level of disturbance $\sigma$ rises. This demonstrates that the uncertainties might affect a subject’s choice of strategy. Government agencies should tightly regulate environmental factors, reduce interference from the outside environment, and establish a platform for green cooperation.

4.2. The Influence of the Government Incentives Strength on the Evolutionary Process

This section explores whether the government incentives to other game subjects act on the coalition’s stability. The strategy evolution of the government, industry, and the UR is simulated by varying the government incentives to enterprises $\alpha$ ($\alpha =0.1, 0.5, 0.9$) and their incentives to academics $\beta$ ($\beta =0.1, 0.5, 0.9$) when other parameters remain as shown in Figure 2.

From a lot of data (see Appendix B), it can be observed in Figure 2 that government incentives for enterprises and the UR fluctuate widely in the interval $\left[0, 0.4\right]$ and $\left[0.8, 1\right]$ when using different values of government incentives $\alpha$ and $\beta$. This suggests that the permissible range of government incentives $\alpha$ and $\beta$ should be between $0.5~0.7$. Government incentives that are too high or too low can make the coalition unstable, which encourages participants to adopt opportunistic behavior patterns.

4.3. The Influence of Media Monitoring Capacity on the Evolutionary Process

In this part, the influence of media monitoring capacity on the stability of the GIUR alliance is explored. With other parameters unchanged, varying the value of media monitoring capacity $\varphi$ ($\varphi =0.1,0.5,0.9$), the path evolution of the government, industry, and the UR as shown in Figure 3.

From a vast quantity of data (see Appendix C for details), it can be observed in Figure 3 that as green technology innovation coalitions evolve, the GIUR alliance tends to have a stable development policy $\left(1, 1, 1\right)$. However, it steadily accelerates with the increase in media monitoring capacity $\varphi$. This implies that the three-game participants change their behavioral plans as a function of their media technologies. In the world, the government is more preoccupied with reputation than are businesses and the UR. When the reputation advantage is low, the government will decide against regulating because it does not stand to gain its own reputation from doing so, while the UR chooses to betray midway.

4.4. The Influence of Product Greenness on Evolutionary Processes

This part mainly explores product greenness’ impact on the stability of the GIUR alliance, and the changing trend of three parties of government, industry, and the UR is simulated as shown in Figure 4 by changing the value of product greenness $\epsilon$ ($\epsilon =0.1, 0.5, 0.9$) with the other parameters unchanged.

From a vast quantity of data (see Appendix D for details), it can be observed in Figure 4 that the government’s choice of alliance strategy is not significantly impacted by a change in product greenness. However, if the product greenness is very low, even though the strategy choice of enterprises and UR will eventually evolve to a stable state, there is a high likelihood that one of them will choose opportunism because of technology spillover gains, etc., and thus choose the strategy of betrayal in the middle of the process. The behavioral strategies of game subjects evolve to $\left(1, 1, 1\right)$ advance more quickly as the value of a product’s greenness $\epsilon$ rises. This highlights how the degree to which a product is green can influence the stability of the alliance, and that the coefficient of product greenness should be kept above 0.5 to safeguard the stability of the Green Innovation Alliance constantly.

4.5. The Influence of Product Greenness on the Capacity of Media Monitoring During Evolution

In this part, the influence of product greenness on the media monitoring capacity in the evolutionary process of the alliance is explored. Numerical variations of product greenness $\epsilon$ ($\epsilon =0.1, 0.5, 0.9$) and media monitoring capacity $\varphi$ ($\varphi =0.1, 0.5, 0.9$), with other parameters held constant, are used to simulate the evolutionary trend of the GIUR alliance’s three parts. The results are shown in Figure 5a–c.

From Figure 5a, it is clear that the government’s strategy will grow with the greenness of the product by progressively converging to 1 when the media monitoring capacity $\varphi$ is extremely modest, but its strategy slowly swings to a non-regulatory strategy due to the high input cost afterward. As the greenness of the product rises and people start to give up choice opt-out opportunities, behavioral tactics used by enterprises and UR will develop into stable methods more quickly. Among them, the UR is slightly less willing to cooperate than the enterprises because of the smaller reputation gain. Compared to Figure 5a–c, with the improvement of media monitoring capabilities, the speed of the three themes in the game into a stable strategy (1,1,1) will also increase. The alliance is more stable when the product greenness $\epsilon$ and the media monitoring capacity $\varphi$ take values over 0.5, as shown by the combination of Figure 3 and Figure 4 (see Appendix C and Appendix D). This indicates that the greenness of the product may increase the R&D revenue of the IUR, which may lead to the strengthening of the cooperation between them and indirectly affect the media monitoring capacity, generating reputation benefits so that the game’s three parties can work together to continuously preserve the stability of the alliance.

4.6. The Influence of Media Monitoring Capacity on the Strength of Government Incentives in the Evolutionary Process

The part mainly discusses the influence of media monitoring capacity on government incentives in the evolution of the alliance. In this part, changing the media monitoring capacity $\varphi$ ($\varphi =0.1, 0.5, 0.9$), the government incentives to industry $\alpha$ ($\alpha =0.1, 0.5, 0.9$), and the incentive to the UR $\beta$ ($\beta =0.1, 0.5, 0.9$) are varied with other parameters held constant, and the GIUR alliance’s strategic evolution process is simulated as shown in Figure 6a–c.

Figure 6a–c show that in the process of the GIUR alliance, changing the values of government incentives $\alpha$, $\beta$, and media monitoring capacity $\varphi$, when the government takes a small incentive from other parties in the game, the media monitoring capacity must be above 0.5 to ensure the stability of the alliance. Too high or too low government incentives will be detrimental to the alliance’s stability at this time. If we do not want the alliance’s stability to change, the media monitoring capacity must be large enough. A significant body of evidence suggests (combined with Appendix B and Appendix C) that a good media monitoring capacity in green technology innovation alliances increases the alliance subjects’ reputation gain, which in turn affects the government incentives to other subjects and ultimately leads to the evolutionary trend of subjects that reputation gain can affect the government incentives to other subjects. The values of government incentives $\alpha$ and $\beta$ vary between $0.5~0.7$, and the media monitoring capacity $\varphi$ is above 0.5. When the advantages acquired by the three sides to the game reach a more balanced state, according to Figure 2, when combined (see Appendix B for details).

5. Discussion

The GIUR green technology innovation has always been one of the important directions of national development and academic research. However, few scholars in the previous literature have comprehensively considered the impact of random uncertainty and media monitoring on the stability of the GIUR innovation alliance. Therefore, this paper introduces Gaussian noise, constructs a stochastic evolution game model of the GIUR, and confirms the model’s validity by giving numerical simulations, as well as the influence of important factors such as media monitoring, uncertain factors, government incentives, and product greenness on the model. This study concludes that the media monitoring ability significantly positively supervises the behavior evolution of the GIUR, which is the same as Geng et al.’s [56] panel data research results. In addition, reducing environmental uncertainty, providing government policy advantages, improving product greenness, and other factors not only meet the needs of human society for characteristic supply chains, manufacturing industries, medicine, and other aspects but also open up the mass consumer market of green products, thus realizing the bilateral sustainable development of the environment and the economy [27,56,57,58].

This paper finds that the higher the product’s greenness, the more it can positively affect the media monitoring capacity, and improving the media monitoring capacity can effectively avoid the crisis of alliance instability caused by improper government incentives. This illustrates when the product’s greenness is not ideal or the incentive policy is not perfect, the government can try its best to coordinate the benefits of all players by creating a good media monitoring capacity, thus solving the problem of breaking the alliance brought by other influencing factors. At the same time, the research of this paper will make the government and other game subjects consider the media benefits from various angles, how to reduce costs and increase reputation benefits at the same time, and bring media monitoring and other factors into more game models to solve social life problems in more fields. Nowadays, as one of the important factors in a country’s development, green innovation technology’s frontier development is mainly in new energy, construction, biology, and industry. In particular, energy conversion is cleaner, more convenient, and more sustainable [59]. In the era when emerging industries are prevalent, it seems that the media not only plays the role of a favorable supervision assistant of the government but also acts as a repository of databases and a discoverer of development frontiers to some extent [60,61]. This provides many new ideas to address the synergistic development of the global economy and environment.

It is worth reflecting on that this study still has several key limitations in the construction of its theoretical framework. First, all parameters of the model’s payment function are derived from empirical literature, which may lead to insufficient adaptability of the model to real-world scenarios. Although sensitivity analysis has verified the stability of these parameters, institutional variables such as government dynamic subsidy mechanisms and the intensity of intellectual property protection have not been included [62], potentially weakening the policy guidance value of the game equilibrium. Second, treating media communication capabilities as exogenous constants overlooks their nonlinear transmission characteristics in the diffusion of innovation, which may underestimate the moderating effect of media monitoring on alliance stability.

The debatable assumptions in the research design also include (1) the decision-making of the three parties is entirely driven by economic interests, without quantifying non-rational factors such as social responsibility, and (2) the benefits of technology transfer are calculated using a linear model, failing to reflect the threshold effect of market acceptance.

Future improvements should focus on breaking through two theoretical constraints: at the methodological level, it is necessary to develop hybrid modeling techniques that integrate fuzzy set theory with stochastic processes, using triangular fuzzy numbers to represent cognitive uncertainties in the payoff matrix; at the empirical dimension, a four-dimensional game framework involving government, industry, universities, and consumers should be established, and case data should be introduced to calibrate the parameters of media dissemination functions. These improvements will not only enhance the model’s explanatory power for complex innovation ecosystems but also provide new analytical perspectives for assessing the critical scale of green technology diffusion.

6. Conclusions

In contrast to the general evolutionary game theory, this paper considers the environmental uncertainty. The stochastic evolutionary game model is used to analyze the equilibrium state of the GIUR alliance members in an uncertain environment, and we also give the judgment theorem of their stable equilibrium solution. Moreover, the influence of various factors on the GIUR dynamic system is verified through numerical simulation, and the conclusions obtained provide theoretical reference for decision makers.

Specifically, this paper considers four key variables: the degree of stochastic interference, government incentives, product green, and media monitoring capabilities, and influences the evolution of the alliance as a continuous variable with almost complete effects. The goal is to further analyze and test the synergy between media monitoring capabilities and government incentives, as well as the greenness of the product. These changes promise to describe high social uncertainty and validate the main effects of game-subject strategy. We found that stochastic interference factors are negatively correlated with the stability of the alliance throughout the evolution of the alliance. However, media monitoring capabilities and product greenness are positively correlated with the stability of the alliance. The green degree of the product will affect the cooperation willingness between enterprises and users so as to attract public opinion and media attention, produce reputation benefits, and promote the improvement of media monitoring ability. If the government’s incentives are too high or too low, they will be detrimental to the stability of the alliance. The improvement of the media monitoring ability is conducive to the development of the game subjects in a better direction.

Based on this, the following suggestions are proposed in this paper. First, improve the external environment. All participants of the GIUR alliance should make every effort to reduce external interference and establish market-oriented operating mechanisms to stabilize the interests of the GIUR alliance. Second, government incentive measures should be more reasonable. In combination with the national conditions, formulate more rational incentive measures to enhance the stability and enthusiasm of the GIUR alliance. Additionally, the GIUR alliance should prioritize green development. All participants should actively promote green technological innovation, improve product greening, and strengthen green cooperation. Finally, the critical role of media should be emphasized. Utilize media to reduce government supervision costs and enhance reputation benefits for all parties.