Unlocking Collaborative Low-Carbon Innovation in Industrial Clusters Environment: A Network Evolutionary Game Approach

Abstract

Numerous small and micro enterprises in Industrial clusters cannot directly participate in low-carbon technology co-innovation cooperation due to their limited technological research and development capabilities, and they need to rely on the diffusion of the results of low-carbon technology co-innovation cooperation in order to obtain the necessary technology and knowledge. However, scientific research is still needed to clarify the diffusion mechanism of cooperative results in a cluster environment and what factors can accelerate the diffusion efficiency. To address this gap, this paper constructs a complex network game model using a scale-free network as its framework. Through simulation analysis, the following conclusions are drawn: (1) Increasing equipment procurement subsidies can promote the diffusion of outcomes, and the larger the cluster, the greater the subsidy required; (2) Increasing carbon emission tax rates can also promote diffusion, but it is necessary to assess corporate affordability based on cluster scale and scientifically formulate tax rates; (3) Carbon tax incentives have limited effects on the diffusion of outcomes, and large-scale clusters exhibit sluggish responses to them; (4) Enhancing cluster management capabilities and fostering distinctive features can promote diffusion, with large-scale clusters demanding even higher standards; (5) Adjusting the prices of low-carbon products has a limited impact on diffusion and is not a sufficient condition; large-scale clusters are insensitive to this factor.

1. Introduction

One of the core elements of high-quality development is the development of a low-carbon economy through low-carbon technological innovation [1,2]. With the rapid development of the new round of industrial change, the Chinese traditional industrialization and R&D organization form is experiencing profound subversion and reshaping, and all the links in the chain of technological innovation are more and more closely connected, which forming an intricate and vibrant network [3,4]. This process has prompted innovation activities to cross the boundaries of a single organization [5], and has promoted various types of innovation subjects to cross the boundaries of fields and move towards a new stage of deep cross-border integration [6,7]. However, due to a series of problems such as insufficient core technologies and R&D strength [8], imperfect policies, regulations and institutional support [9], and unsound market mechanisms and incentives [10], it is difficult to promote the collaborative innovation process of low-carbon technologies in existing enterprises. Therefore, it is particularly important to construct and promote a number of platforms and systems aimed at accelerating the collaborative innovation of low-carbon technologies in enterprises, both from the overall perspective of macroeconomic and social development and at the micro level of enterprises’ own growth and transformation.

The success of low-carbon technology innovation depends on effective sharing and collaboration among stakeholders [11,12]. However, in the process of collaborative innovation of low carbon technology in enterprises, there are great differences between the heterogeneous subjects in terms of resource conditions, core technology and division of labor, and it is this difference that has an immeasurable effect on the process of collaborative innovation [13,14]. Therefore, the construction of an efficient and rational technology innovation platform and ecosystem is crucial to support the collaborative innovation activities of enterprises in low-carbon technologies [15,16]. Industrial clusters are a reasonable form of industrial organization formed by the agglomeration effect, which is a common phenomenon in the process of industrialization [17]. In the context of knowledge economy, cluster-based technological innovation can promote the exchange of knowledge between industries and promote the development of industrial structure [18]. Meanwhile, as key hubs of regional production and innovation, the resource integration and innovation capabilities of industrial clusters are self-evidently powerful [14]. Specifically, the industrial clusters with the characteristics of division of labor production mode and agglomeration innovation can lay a solid foundation for the low carbon technology co-innovation of enterprises [19], which can not only promote the effective integration of innovation resources, but also create favorable conditions for the smooth industrialization and marketization of the results of co-innovation. Therefore, if enterprise low-carbon technology co-innovation is deeply integrated with industry cluster platforms, it will undoubtedly greatly promote the concentration and optimization of innovation resources and accelerate the process of co-innovation. Figure 1 illustrates a complete technological innovation system for an industry cluster.

Innovation in industrial clusters relies heavily on the combination of knowledge among cluster enterprises with optimal levels of cognitive proximity [20]. However, in the cluster environment, a large number of start-ups, small and micro enterprises cannot directly participate in low-carbon technology co-innovation cooperation due to their limited technological research and development capabilities, and they need to rely on the diffusion of the results of low-carbon technology co-innovation cooperation in order to obtain the necessary technology and knowledge. Existing research points out that while all enterprises can strive to become more competitive through innovation, the effects of diffusion of innovation will ultimately limit their growth [21]. The cluster enterprises should not only cultivate and optimize their innovation networks, but also improve their technological learning capabilities [22], and thus enhance the efficiency of low-carbon technologies diffusion [23], realize the sustainable pursuit of economic and ecological benefits [24]. Consequently, if the network structure within industrial clusters can be fully utilized [25], relying on its close network connection [26], the cooperative results achieved by low-carbon technology co-innovation can be diffused to those small and medium-sized enterprises that are difficult to participate in co-innovation due to the limitation of technological strength, which can not only promote the optimal allocation of technological innovation resources, but also greatly enhance the level of low-carbon technological innovation of the whole industrial chain, and achieve the sharing of the innovation results for all, which is no less significant than low-carbon technology co-innovation itself [27,28].

Therefore, based on the above analysis, this paper intends to construct a complex network evolutionary game model on the basis of clarifying the network topology and evolution rules of the diffusion of low-carbon technology collaborative innovation cooperation results of enterprises in the cluster environment, and analyze it through simulation, so as to come up with the diffusion scheme of the low-carbon technology collaborative innovation cooperation results of enterprises in the cluster environment.

The emphasis of this paper is on three key research questions: (1) What are the network topology and evolution rules for the diffusion of enterprises’ low-carbon technology co-innovation cooperation results in the industrial cluster environments? (2) What factors can influence the diffusion efficiency of enterprises’ low-carbon technological innovations in an industrial cluster environment? (3) Whether different factors have different impacts on the diffusion of low-carbon technology co-innovation outcomes in industrial cluster networks of different sizes?

Finally, based on the comprehensive analysis of the results, this paper puts forward some countermeasures for managerial and policy implications. The following summarizes the main contributions of this work:

(1)

Combining enterprise low-carbon technology innovation with industrial clusters, and fully considering the impact of the network structure of industrial clusters on low-carbon technology diffusion.

(2)

According to the network topology and evolutionary rules of the enterprises’ low-carbon technology collaborative innovation cooperation results diffusion in the industrial cluster environment, and analyze the actual impact of relevant factors on the diffusion of cooperation results.

(3)

Based on the in-depth analysis of the research results, a reasonable and effective program for the diffusion of low-carbon technological innovations has been designed.

The remainder of this paper is organized as follows: Section 2 reviews the relevant literature and introduces the main contribution of this paper. Section 3 details the basic assumptions and relevant parameters, and constructs a complex network evolutionary game model. Section 4 verifies the interaction of strategy choice among game participants and related influencing factors through parameter assignment and software simulation. Section 5 summarizes the research conclusions and engages in discussion with existing studies. Section 6 formulates corresponding countermeasures based on research conclusions. Section 7 outlines the limitations of this paper and prospects for future research.

2. Literature Review

In this section, three separate but intertwined strands of research related to this paper are mainly reviewed: (1) Low-carbon technology innovation; (2) Technological innovation in industrial clusters; (3) Conflicts and contradictions in low-carbon technology innovation.

2.1. Low-Carbon Technology Innovation

The urgency of global climate change is driving companies to focus on low-carbon strategies to enhance their environmental performance [29]. Therefore, in the era of a low-carbon economy, actively investing in various low-carbon technologies to reduce carbon emissions is a crucial measure for enterprises to respond to changes in the external environment [30]. Afandi believed that economic agglomeration, structural upgrading, and innovation networks are important channels for promoting low-carbon transformation in enterprises [31]. Lyu argued that enhancing management capabilities, R&D capabilities, and environmental information disclosure capabilities are key channels influencing low-carbon technological innovation [32]. Gu et al. analyzed the specific impact of the external policy environment on corporate low-carbon technological innovation [9].

However, low-carbon technological innovation is characterized by high costs and significant risks, which result in relatively low innovation efficiency [7]. Therefore, it is crucial to establish a low-carbon technology innovation ecosystem led by the government and driven by enterprises as the primary innovators [33]. T. Shi et al. pointed out that the government should expand subsidies for collaborative innovation in low-carbon technologies among enterprises [34]. Z. Wang et al. believes that subsidies should not be static; dynamically adjusted policies can significantly increase the adoption of low-carbon technologies [35]. Moreover, with the advancement of the digital economy, exploring feasible pathways for low-carbon digital development has also become a hot topic of the moment [36]. Yao et al. emphasized that enterprise digital transformation can reshape business processes, thereby reducing energy consumption [29]. Chang pointed out that digitalization plays a significant role in promoting low-carbon transformation for enterprises [37]. Hou et al. discovered that knowledge reconstruction can serve as an intermediary between digital transformation and low-carbon technological innovation [38].

2.2. Technological Innovation in Industrial Clusters

Industrial clusters represent a rational form of industrial organization and an effective means of spatial competition [39]. In the context of the knowledge economy, clustered technological innovation can facilitate knowledge exchange across industries and advance industrial restructuring [40]. Chen analyzed the construction of digital innovation ecosystems for advanced manufacturing clusters [14]. Meng et al. pointed out that green and low-carbon development in industrial parks plays a significant role in promoting industrial technology clustering [41]. Meanwhile, with the rapid advancement of artificial intelligence technology, AI-driven innovation has become a key driver of economic growth within manufacturing clusters [42]. Yang et al. believed that AI-driven industrial clustering does not develop naturally but requires policy-driven initiatives [43]. Lazzeretti et al. explored the innovation potential of artificial intelligence ecosystems within industrial clusters [44]. Moreover, since industrial clusters serve as effective organizational vehicles for disseminating innovation outcomes, it is essential to specifically examine how the network structure of industrial clusters and government subsidies contribute to technological diffusion within these clusters [45]. Ge et al. examined the community structure of collaborative networks within patent-intensive industrial clusters and the distinctive characteristics they exhibit [46]. Wang et al. analyzed the impact of corporate strategic decisions on the dissemination of low-carbon technologies in industrial clusters [47]. Pan et al. believed that mandatory policies and fiscal subsidies can effectively increase the adoption rate of green technologies within industrial clusters [48].

2.3. Conflicts and Contradictions in Low-Carbon Technology Innovation

The success of low-carbon technological innovation depends on effective sharing and collaboration among stakeholders [11]. However, due to fundamental differences in objectives among participating entities, conflicts over low-carbon technological innovation persist [49]. Specifically, as public administrators, governments pursue overarching emission reduction targets and energy transitions, seeking to steer technological development through policy guidance [50].

However, as market entities, enterprises prioritize profit maximization and often favor developing incremental technologies that yield rapid market returns over disruptive innovations requiring long-term investment [51]. Therefore, the fundamental solution to resolving structural contradictions in low-carbon technological innovation lies in establishing institutionalized coordination and interest-balancing mechanisms to guide diverse stakeholders toward collaborative evolution. Evolutionary game theory treats the adjustment process of group behavior as a dynamic system [52], separately describing individual actions and their relationship with the group, thereby constructing macro models grounded in micro foundations [53]. Consequently, evolutionary game theory has been widely applied to analyze cooperation and conflict issues in low-carbon technological innovation. Luo et al. employed evolutionary game theory to examine the strategies of stakeholders in the development of agricultural green technology innovation systems [54]. T. Shi et al. employed evolutionary game theory to analyze the issue of value co-creation within low-carbon technological innovation ecosystems [37]. Zhou et al. analyzed the impact of horizontal competition and government regulation on corporate low-carbon technological innovation using evolutionary game theory [55].

2.4. Research Gaps and Our Contribution

While the extant literature has robustly established the positive correlation between industrial clusters and innovation, the micro-level mechanisms through which policy interventions effectively stimulate low-carbon transitions within these clusters remain underspecified, particularly from a theoretical modeling perspective. A significant gap lies in the simplifying assumptions commonly adopted in prior analytical models. For instance, many studies assume cluster homogeneity or model enterprises as isolated decision-makers, thereby overlooking the critical role of strategic interactions among heterogeneous enterprises and the effect of cluster size on policy outcomes. This theoretical oversimplification limits our understanding of how policies can be tailored to different cluster contexts.

Therefore, to fill this gap, this paper constructs a complex network evolutionary game model to investigate the diffusion of low-carbon technological innovations among manufacturing enterprises in industrial clusters. The study explicitly defines the network’s topology and the rules governing its evolution. It employs a scale-free network for computational simulations, with the aim of deriving effective diffusion strategies applicable across clusters of diverse sizes. The specific model construction and associated research assumptions are detailed in the following text.

3. Material and Method

3.1. Problem Description

The essence of an economic system is a network of economic organizations connected on the basis of direct inter-organizational relationships. Low-carbon technology diffusion needs to be built under complex socio-economic systems, and the relationships of potential adopting enterprises in cluster environments are an important diffusion channel for low-carbon technologies. Existing studies have pointed out that the nodes of a large number of realistic networks obey a power distribution, i.e., they obey the structural characteristics of scale-free networks. Therefore, this paper will use the BA scale-free network as a carrier to study the diffusion of low-carbon technology co-innovation cooperation results of manufacturing enterprises in a cluster environment. Based on Bass theory, it is known that an innovative technology can be diffused through both word-of-mouth (internal) and mass communication (external) [56]. Therefore, in the collaborative innovation of low-carbon technologies among enterprises in a cluster environment, when new technological achievements appear, they can initially attract some pioneering enterprises to adopt them through mass dissemination, and then form an initial network for technology diffusion. After that, by virtue of the word-of-mouth effect, more enterprises are attracted to participate until the technology innovation diffusion network stabilizes. Therefore, with reference to the study of [57], this paper maps the evolutionary system of the diffusion of enterprises’ low-carbon collaborative innovation cooperation results in a cluster environment, as shown in Figure 2.

As shown in Figure 2, it can be found that there are three circles in the evolutionary system of low-carbon technology cooperation and innovation among enterprises in the whole industrial cluster environment. Among them, the central circle, is the leading enterprises carrying out low-carbon technology co-innovation. The first and second circles, on the other hand, are small and medium-sized enterprises (SMEs) that are not able to participate directly in low-carbon technological innovations, with the difference being that enterprises in the first circle are more closely linked to the central circle. Enterprises in different circles are connected to each other, and the purpose of the whole evolutionary system is to diffuse the results of low-carbon technology co-innovation to the whole cluster environment through the network of connections between enterprises.

Therefore, based on the characteristics of BA scale-free networks as described above, this paper constructs a diffusion network $G\left(V,E\right)$ for collaborative innovation outcomes of low-carbon technologies among manufacturing enterprises in a cluster environment. Among them, $V$ represents all manufacturing enterprises that may adopt low-carbon technologies, while $E$ denotes the direct relationships among all manufacturing enterprises that may adopt low-carbon technologies. Assuming mutual influence exists among manufacturing enterprises within a cluster environment, this implies that only one edge exists between any two nodes in the network, and each edge is undirected. If $e_{ij}=1$, then there is an edge between nodes $i$ and $j$; conversely, if $e_{ij}=0$, then there is no edge between nodes $i$ and $j$, meaning there is no direct relationship. This paper primarily employs metrics such as degree distribution, average clustering coefficient, and average path length to characterize the topological features of collaborative innovation networks for low-carbon technologies within a clustered environment. If node enterprise $i$ is connected to $k_i$ potential adopter enterprises, then $k_i$ is considered the degree of node enterprise $i$. Assume that in a manufacturing enterprise low-carbon technology collaborative innovation network within a cluster environment, there are $m_0$ potential adopter enterprises. Newly added $n$ potential adopter enterprises connect with existing $m\left(m<m_0\right)$ node enterprises at a probability of $p$, until the number of nodes in the network stabilizes. Among these, the expression for probability $p$ is shown in Equation (1).

$$p\left(i\right)={\displaystyle \frac{k_i}{\sum _j{k}_j}}$$

(1)

This paper employs a decision-making model based on the Fermi rule, whose core lies in characterizing the degree of bounded rationality under imperfect information through the noise parameter $\sigma$. Compared to the commonly used Logit rule and proportional imitation rule, the Fermi rule possesses unique advantages in terms of mechanism and realism, making it more suitable for the context of this study, as expressed by the specific functional form shown in Equation (2).

$$F_{N_i\leftarrow N_j}={\displaystyle \frac{1}{1+\exp \left[\left(S_i-S_j\right)/\sigma \right]}}$$

(2)

Among Equation (2), $N_i$ and $N_j$ represent the strategic choices of enterprise $i$ and enterprise $j$ in the game, respectively, while $S_i$ and $S_j$ denote the cumulative profits of enterprise $i$ and enterprise $j$, respectively. $\sigma \left(\sigma ⩾0\right)$ represents the noise effect, indicating the likelihood that manufacturing enterprises in a cluster environment may make irrational choices. The closer the value of $\sigma$ approaches 0, the greater the likelihood that enterprises will make rational choices. If the competitor’s returns are superior, the enterprise will adopt their strategy; otherwise, it will maintain its original strategy. The larger the value of $\sigma$, the noisier the environment in which the enterprise operates, leading the enterprise to randomly select its own game strategy. Referencing the research by Wang [58], this chapter sets the noise level to $\sigma =0.1$.

3.2. Basic Model Settings and Assumptions

Assumption 1.

After the core enterprises in the cluster environment have successfully cooperated in low-carbon technology co-innovation, enterprises in the cluster environment that have not participated in low-carbon technology co-innovation have two strategy options, namely, “acceptance” strategy and “non-acceptance” strategy. When enterprises choose the “accept” strategy, they will adopt the results of low-carbon technology co-innovation cooperation, improve their own production technology level, and reduce carbon emissions. While when enterprises choose the “non-acceptance” strategy, they will not adopt the results of low-carbon technology co-innovation cooperation, and will still use the traditional technology to reduce carbon emissions. In addition, when enterprises choose the “non-acceptance” strategy, their carbon footprint doesn’t decrease.

Assumption 2.

When the enterprise chooses the “acceptance” strategy, it will adopt low-carbon production technology for production, so let the production cost of the product produced by low-carbon production technology is $c_n$, the sales price is $p_n$. When the enterprise chooses the “non-acceptance” strategy, it adopts the traditional production technology for production, so let the production cost of the product produced by the traditional production technology is $c_t$, and the sales price is $p_t$. In addition, let $Q$ represent the total output of products produced by enterprises in the cluster environment, i.e.,:

$$Q=q_t+q_n$$

(3)

Among Equation (3), $q_t$ represents the total output of products produced with traditional production techniques, $q_n$ represents the total output of products produced with low carbon production techniques.

Assumption 3.

Due to the process of diffusion of the results of collaborative innovation cooperation in low-carbon technologies, there will be a corresponding change in consumer preferences for low-carbon products. Therefore, with reference to the research of Zeng et al. [59], this paper let $\omega \left(t\right)$ represent the consumer’s preference for low-carbon products at moment $t$, i.e.,:

$$\omega \left(t\right)=\omega \left(0\right)+\lambda \left(1-\omega \left(0\right)\right)\left(H_n\left(t\right)-H_n\left(0\right)\right)$$

(4)

Among Equation (4), $\omega \left(0\right)$ represents the initial consumer preference for low-carbon products, $H_n\left(t\right)$ represents the proportion of enterprises that choose the “acceptance” strategy to low-carbon technologies in the cluster environment at time $t$, $H_n\left(0\right)$ represents the initial proportion of low-carbon technology enterprises that choose the “acceptance” strategy in cluster environments, $\lambda$ represents the consumer preference adjustment factor for low-carbon products. Therefore, based on the above statements, we can derive the specific expressions for $q_t$ and $q_n$, as shown in Equations (5) and (6).

$$q_t=\omega \left(t\right)Q/H_n\left(t\right)N$$

(5)

$$q_n=\left(1-\omega \left(t\right)\right)Q/\left(1-H_n\left(t\right)\right)N$$

(6)

Among Equations (5) and (6), $N$ represents the total number of enterprises in the clustered environment, and the meanings of $\omega \left(t\right)$, $Q$ and $H_n\left(t\right)$ have been explained in the preceding text.

Assumption 4.

When a significant number of enterprises in a cluster environment choose the “acceptance” strategy, a low-carbon technology production ecology will be formed, and such a low-carbon production ecology will bring additional benefits to enterprises in the cluster environment. Therefore, with reference to the research of Li et al. [57], this paper let $E\left(t\right)$ represent the low-carbon ecological levels in cluster environments at moment $t$, i.e.,:

$$E\left(t\right)=E\left(0\right)+\theta \left(H_n\left(t\right)-H_n\left(0\right)\right)$$

(7)

Among Equation (7), $E\left(0\right)$ represents the initial low-carbon ecological level of the cluster environment, $\theta$ represents the cluster environment low-carbon ecological-building conversion rate, which is closely related to factors such as the level of management and the degree of specialization and distinctiveness of the cluster environment. In addition, when enterprises choose to accept the cooperative results of low-carbon technology co-innovation, they will obtain additional benefits due to the low-carbon technology production ecology formed by the cluster environment, so let the additional benefit coefficient be $\phi$. On the contrary, when enterprises choose not to accept the cooperative results of low-carbon technology co-innovation, this low-carbon ecology will cause certain additional losses to the enterprise, so set the additional loss coefficient as $\eta$ (when a critical mass of enterprises adopt low-carbon technologies, the competitive landscape within the industry will be reshaped. New rules will reward compliant players and penalize laggards).

Assumption 5.

Let $T$ represents the carbon emissions per unit of products produced by enterprises producing products with traditional production techniques, and $T\prime$ represents the carbon emissions per unit of products produced by enterprises producing products with low-carbon production techniques. Therefore, it satisfies $T\prime <T$. Meanwhile, the government will tax the carbon emissions of enterprises at the corresponding tax rate, so set the carbon emission tax rate as $\alpha$, enterprises that produce products with low-carbon production technology will receive certain tax incentives, so set the incentive coefficient as $\beta$. In addition, if enterprises choose the “acceptance” strategy and adopt the collaborative outcomes of low-carbon technology co-innovation, they will also incur an additional equipment acquisition cost, denoted $I_n$. And the government will also subsidize the purchase of low-carbon production equipment by enterprises, so set the subsidy coefficient as $\gamma$.

Assumption 6.

When both sides of the game choose the “acceptance” strategy or one side chooses the “acceptance” strategy and the other side chooses the “non-acceptance” strategy, the benefits of enterprises choosing the “acceptance” strategy can be expressed as $U_{CN}$, the benefits of enterprises choosing the “non-acceptance” strategy can be expressed as $U_{TN}$, and when both sides of the game choose the “non-acceptance” strategy, the enterprises’ payoff can be expressed as $U_{TNN}$. The specific expressions are shown in Equations (8)–(10) (the meaning of the relevant parameters has been explained in the preceding text), i.e.,:

$$U_{CN}=\left(p_n-c_n\right)q_n+\phi E\left(t\right)-\left(1-\beta \right)\alpha T\prime q_n-\left(1-\gamma \right)I_n$$

(8)

$$U_{TN}=\left(p_t-c_t\right)q_t-\eta E\left(t\right)-\alpha T{q}_t$$

(9)

$$U_{TNN}=\left(p_t-c_t\right)q_t-\alpha T{q}_t$$

(10)

Therefore, based on the above research assumptions, this paper constructed a complex network game model. The specific meanings of the relevant parameters are shown in

Table 1. List of parameter meanings of complex network game models.

Parameters	Meanings	Value Range
$U_{CN}$	When both parties in the game simultaneously choose the “acceptance” strategy, or when one party chooses the “acceptance” strategy while the other chooses the “non-acceptance “strategy, the enterprise that selected the “acceptance” strategy will gain.
$U_{TN}$	When one party in the game chooses the “acceptance” strategy and the other chooses the “non-acceptance” strategy, the enterprise that selects the “non-acceptance” strategy gains
$U_{TNN}$	When both parties in the game simultaneously choose the “non-acceptance” strategy, the profit of the enterprise that adopts the “non-acceptance” strategy
$c_n$	Production costs of products produced with low-carbon production technologies	$c_n>0$
$p_n$	Selling price of products produced with low-carbon production technologies	$p_n>0$
$q_n$	Total output of products produced with low-carbon production technologies	$q_n>0$
$c_t$	Production costs of products manufactured using traditional production technologies	$c_t>0$
$p_t$	Selling price of products produced with low-carbon production technologies	$p_t>0$
$q_t$	Total output of products produced with traditional production techniques	$q_t>0$
$Q$	Total output of products produced by enterprises in a clustered environment	$Q=q_t+q_n>0$
$\omega \left(t\right)$	Consumer Preferences for Low-Carbon Products at moment $t$	$\omega \left(t\right)>0$
$\omega \left(0\right)$	Initial consumer preferences for low-carbon products	$\omega \left(0\right)>0$
$H_n\left(t\right)$	Proportion of enterprises in cluster environments that have accepted low-carbon technologies at moment $t$	$H_n\left(t\right)>0$
$H_n\left(0\right)$	Initial proportion of enterprises in cluster environments that have accepted low-carbon technologies	$H_n\left(0\right)>0$
$\lambda$	Consumer preference adjustment factor for low-carbon products (The higher $\lambda$ value, the stronger the green preference)	$0<\lambda <1$
$N$	Total number of enterprises in the clustered environment	$N>0$
$E\left(t\right)$	Low-carbon ecological levels in cluster environments at moment $t$	$E\left(t\right)>0$
$E\left(0\right)$	Initial low-carbon ecological level of the cluster environment	$E\left(0\right)>0$
$\theta$	Cluster environment low carbon eco-build conversion rate (The higher $\theta$ value, the stronger the low carbon eco-build conversion rate)	$0<\theta <1$
$\phi$	Benefit coefficients for additional benefits from low-carbon technology production ecologies in cluster environments (The higher $\phi$ value, the greater the additional benefits)	$0<\phi <1$
$\eta$	Loss factor for additional losses due to low-carbon technology production ecology in cluster environments (The higher $\eta$ value, the greater the additional losses)	$0<\eta <1$
$T$	Carbon emissions per unit of product produced by enterprises producing products using traditional production techniques	$T>0$
$T\prime$	Carbon emissions per unit of product produced by enterprises producing products with low-carbon production technologies	$0<T\prime <T$
$\alpha$	Carbon tax rate at which the government collects taxes on carbon emissions from enterprises (The higher the value of $\alpha$, the higher the tax)	$0<\alpha <1$
$\beta$	Government tax incentive coefficients for enterprises producing products with low-carbon production technologies (The higher the value of $\beta$, the greater the tax incentive)	$0<\beta <1$
$I_n$	Additional equipment acquisition costs for enterprises producing products with low-carbon production technologies	$I_n>0$
$\gamma$	Government purchase subsidy factor for enterprises purchasing additional equipment for low-carbon production (The higher the value of $\gamma$, the higher the subsidy)	$0<\gamma <1$

, and the game payment matrix is shown in

Table 2. Game payment matrices for complex network games.

		$\mathbf{Enterprise} \mathit{B}$
		“Acceptance” Strategy	“Non-Acceptance” Strategy
Enterprise $A$	“Acceptance” strategy	$U_{CN}=\left(p_n-c_n\right)q_n+\phi E\left(t\right)-\left(1-\beta \right)\alpha T\prime q_n-\left(1-\gamma \right)I_n$ $U_{CN}=\left(p_n-c_n\right)q_n+\phi E\left(t\right)-\left(1-\beta \right)\alpha T\prime q_n-\left(1-\gamma \right)I_n$	$U_{CN}=\left(p_n-c_n\right)q_n+\phi E\left(t\right)-\left(1-\beta \right)\alpha T\prime q_n-\left(1-\gamma \right)I_n$ $U_{TN}=\left(p_t-c_t\right)q_t-\eta E\left(t\right)-\alpha T{q}_t$
	“Non-acceptance” strategy	$U_{TN}=\left(p_t-c_t\right)q_t-\eta E\left(t\right)-\alpha T{q}_t$ $U_{CN}=\left(p_n-c_n\right)q_n+\phi E\left(t\right)-\left(1-\beta \right)\alpha T\prime q_n-\left(1-\gamma \right)I_n$	$U_{TNN}=\left(p_t-c_t\right)q_t-\alpha T{q}_t$ $U_{TNN}=\left(p_t-c_t\right)q_t-\alpha T{q}_t$

.

Based on Equations (8)–(10), we can derive the payoff matrix for the game, as shown in Table 2. This matrix defines the payoff outcomes for enterprises under all possible strategy combinations and serves as the foundation for solving the game equilibrium. The rows of the matrix represent the strategy choices of enterprise A, while the columns represent the strategy choices of enterprise B. Each pair of numbers within a cell corresponds to the payoffs for enterprise A and enterprise B under that specific strategy combination.

3.3. Parametric Simulation Steps and Network Diffusion Benchmarks

In order to compare the simulation results under different conditions, and then dig out the key factors affecting the diffusion of the cooperative achievements of low-carbon technology collaborative innovation of manufacturing enterprises in the cluster environment, this paper uses simulation software to simulate the diffusion process of the cooperative achievements of low-carbon technology collaborative innovation of manufacturing enterprises in the cluster environment, and the specific simulation steps are shown in Figure 3.

To realize the aforementioned complex network evolutionary game model, we designed a simulation program comprising the following five steps, drawing upon relevant literature [57,60]:

Step 1: According to the parameter settings, given an initialized scale-free network $G\left(V,E\right)$ for the diffusion of low-carbon technology collaborative innovation results of manufacturing enterprises in a cluster environment;

Step 2: The initial strategy is randomly assigned to each enterprise node in the diffusion network of low-carbon technology collaborative innovation results, and the game payment matrix is constructed;

Step 3: Start a game;

Step 4: Enterprises in the diffusion network of low-carbon technology collaborative innovation cooperation results randomly select neighboring enterprises for comparison of game benefits, and at the same time update the game strategy according to the comparison rules described in the previous section;

Step 5: Go to step 3 until the end of the scheduled simulation time.

Based on the above parameter settings, a benchmarking model of network diffusion of low-carbon technology collaborative innovation achievements of manufacturing enterprises in a cluster environment can be constructed, and the evolution of the enterprises’ gaming strategies under scale-free networks can be further demonstrated. As shown in Figure 4, this paper considers the diffusion of cooperative outcomes in two cases, $N=50$ as well as $N=100$, for the number of node firms in the cluster environment. Specifically, the green nodes represent enterprises that have accepted the results of low-carbon technology co-innovation, while the white nodes indicate enterprises that did not accept the results of low-carbon technology co-innovation.

Moreover, the fundamental differences in network structure between the distinct cluster sizes represented in Figure 4a (50-node enterprises) and Figure 4b (100-node enterprises) will theoretically influence the dynamics of game interactions and technology diffusion. Consequently, this paper will simulate the diffusion of low-carbon technologies across cluster environments with varying node counts through parameterized simulations.

4. Results and Discussion

Based on the above analysis, this paper adopts the method of numerical simulation to further validate the influence of relevant parameters on the strategic choices of game participants, with a view to providing suggestions and countermeasures for the diffusion of the cooperative results of low-carbon technology collaborative innovation among manufacturing enterprises in the cluster environment. Therefore, referring to Zeng et al. [59] for relevant cost and price settings in the dissemination of green technologies, and Li et al. [57] and Wu et al. [60] in relation to carbon tax and network structure settings, this paper assigns preliminary values to the parameters in the model, as shown in

Table 3. Initial assignment of parameters to complex network game models.

Parameters	$c_n$	$p_n$	$c_t$	$p_t$	$H_n\left(0\right)$	$\omega \left(0\right)$	$Q$	$N$	$\lambda$	$E\left(0\right)$
Value	1	2	0.2	0.8	0.1	0.3	300	50/100	0.2	0.2
Parameters	$\theta$	$\phi$	$\eta$	$\alpha$	$\beta$	$T$	$T\prime$	$I_n$	$\gamma$
Value	0.8	0.8	1.2	0.2	0.05	3	1	5	0.2

Notes: the theoretical definitions for all parameters in this table are provided in full within Table 1.

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4.1. Impact of Changes in the Government Purchase Subsidy Factor for Enterprises Purchasing Additional Equipment for Low-Carbon Production on the Diffusion of Cooperation Results

Figure 5 represents the impact of changes in the government purchase subsidy factor for enterprises purchasing additional equipment for low-carbon production $\gamma$ on the diffusion of cooperation results.

As shown in Figure 5, changes in the coefficient of subsidies for the acquisition of low-carbon production equipment by enterprises $\gamma$ have a significant impact on the diffusion results of low-carbon technological collaborative innovation achievements of enterprises in the cluster environment, and the diffusion results vary under different network sizes. Specifically, under the scale-free network of $N=50$, the diffusion rate of low-carbon technology co-innovation among manufacturing enterprises in the cluster environment will increase with the increase of the subsidy coefficient for the purchase of low-carbon production equipment. And under the scale-free network of $N=100$, although the simulation result is still that increasing the acquisition subsidy coefficient can increase the diffusion ratio of low-carbon technology co-innovation results, it is worth noting that the diffusion ratio of low-carbon technology co-innovation results tends to be close to zero under the same numerical condition (i.e., $\gamma =0.05,0.1,0.15,0.2$). It can be concluded that increasing subsidies for the purchase of low-carbon production equipment by enterprises can increase the diffusion rate of low-carbon technology co-innovation results, but the exact amount of the purchase subsidy cannot be generalized and needs to be taken into account in the specific circumstances of the cluster environment. The larger size of the network in a cluster environment, the greater subsidy required for the acquisition of low-carbon production equipment.

4.2. Impact of Changes in Government Tax Incentive Coefficients for Enterprises Producing Products with Low-Carbon Production Technologies on the Diffusion of Cooperation Results

Figure 6 represents the impact of government tax incentive coefficients for enterprises producing products with low-carbon production technologies $\beta$ on the diffusion of cooperation results.

As shown in Figure 6, the effects of changes in carbon tax incentive coefficients on the diffusion outcomes of low-carbon technology co-innovation results of manufacturing enterprises in cluster environments vary across network sizes. Specifically, under the scale-free network of $N=50$, the diffusion rate of low-carbon technological cooperation and innovation achievements of enterprises in the cluster environment will be higher and higher with the increase of the carbon emission tax incentive coefficient. In contrast, under the scale-free network of $N=100$, increasing the carbon tax credit does not increase the diffusion ratio of the results of collaborative innovation in low-carbon technologies. It can be concluded that carbon tax incentives are more effective in increasing the diffusion rate of low-carbon technology co-innovation in small cluster environments, while larger cluster environments are not sensitive to this. Therefore, in promoting the diffusion of low-carbon technologies among manufacturing enterprises in cluster environments, relevant government departments should analyze the situation on a case-by-case basis. In addition to providing tax incentives for carbon emissions, they should be complemented by other relevant policies.

4.3. Impact of Changes in Cluster Environment Low Carbon Eco-Build Conversion Rate on the Diffusion of Cooperation Results

Figure 7 represents the impact of cluster environment low carbon eco-build conversion rate $\theta$ on the diffusion of cooperation results.

As shown in Figure 7, the change of the subsidy coefficient of enterprises’ acquisition of low-carbon production equipment has a significant positive impact on the diffusion results of low-carbon technology collaborative innovation cooperation results of enterprises in the cluster environment, and the impact effect varies under different network sizes. Specifically, under the scale-free network of $N=50$, the diffusion of low-carbon technology co-innovation achievements of manufacturing enterprises in the cluster environment can be promoted when $\theta =0.5,0.8$, while the diffusion rate of low-carbon technology co-innovation achievements will increase rapidly when $\theta ⩾1$. While under the scale-free network of $N=100$, although the simulation result is still that increasing the conversion rate of low-carbon ecological construction of cluster environment $\theta$ can increase the diffusion rate of low-carbon technology collaborative innovation results, it is worth noting that the conversion rate of low-carbon ecological construction of cluster environment can show an upward trend only if $\theta =3$. It can be concluded that increasing the level of management, specialization and characterization in the cluster environment and thus improving the conversion rate of low-carbon ecological construction in the cluster environment can promote the diffusion of low-carbon technological collaborative innovation achievements of enterprises in the cluster environment, especially the larger cluster environment, which has higher requirements for the conversion rate of low-carbon ecological construction.

As shown in Figure 8, when the value of $\theta$ is relatively high (i.e., $\theta =3$), adjusting the value of $\beta$ reveals that even a low value of $\beta$ can facilitate the diffusion of collaborative innovation outcomes in low-carbon technologies within the cluster environment. This demonstrates that in large clusters, the longer information-transmission chains dilute the marginal effect of government tax incentive coefficients $\beta$. Therefore, combining government tax incentive coefficients $\beta$ with ecological construction (higher θ) will shorten the information path and restores policy effectiveness.

4.4. Impact of Changes in Carbon Tax Rate at Which the Government Collects Taxes on Carbon Emissions from Enterprises on the Diffusion of Cooperation Results

Figure 9 represents the impact of carbon tax rate at which the government collects taxes on carbon emissions from enterprises $\alpha$ on the diffusion of cooperation results

As shown in Figure 9, increasing the carbon tax rate can promote the diffusion of cooperative outcomes of low-carbon technology collaborative innovation among enterprises in a cluster environment, but the sensitivity of the carbon tax rate to the diffusion of cooperative outcomes varies at different network sizes. Specifically, under the scale-free network of $N=50$, the diffusion of low-carbon technology co-innovation results of enterprises in the cluster environment can be promoted when $\alpha ⩾0.2$. While under the scale-free network of $N=100$, $\alpha ⩾0.3$ is required. Based on this finding, it can be concluded that increasing the carbon emission tax rate can constrain the business behavior of enterprises and thus promote the diffusion rate of low-carbon technology collaborative innovation achievements. However, due to the different sizes of cluster environments, different cluster environments have different tolerances for carbon emission tax rates. Meanwhile, combined with the previous discussion on $\beta$, it can also be observed that enterprises within small-scale clusters typically face more severe resource and capability constraints, resulting in lower initial “absorption capacity”. Consequently, even limited subsidies or carbon taxes can significantly alter their cost-benefit calculations, providing a critical impetus sufficient to cross the threshold for technology adoption. The marginal effects of such policies are notably pronounced. Conversely, enterprises within large-scale clusters frequently possess robust absorption capacity and redundant resources. External policy shocks exert relatively minor impacts relative to their operational scale, rendering them “insensitive”. Therefore, the relevant government departments need to formulate a reasonable and effective policy after a comprehensive research and assessment, in order to promote the proliferation of the results of collaborative innovation and cooperation in low-carbon technology among enterprises in the cluster environment.

4.5. Impact of Changes in Selling Price of Products Produced with Low-Carbon Production Technologies on the Diffusion of Cooperation Results

Figure 10 represents the impact of selling price of products produced with low-carbon production technologies $p_n$.

As shown in Figure 10, changes in the sales price of enterprises’ low-carbon products have a significant impact on the diffusion results of low-carbon technology collaborative innovation achievements of enterprises in cluster environments, and the diffusion results vary under different network sizes. Specifically, under the scale-free network of $N=50$, when the sales price of low-carbon products of enterprises is $p_n=1.5$, the results of low-carbon technology co-innovation cannot be diffused within the cluster environment, while when $p_n=2,2.5$ can promote the diffusion of low-carbon technology co-innovation results of enterprises in the cluster environment. Under the scale-free network of $N=100$, increasing the sales price of enterprises’ low-carbon products within a reasonable range can promote the diffusion of low-carbon technological collaborative innovation achievements of enterprises in the cluster environment, but the diffusion strength cannot reach the diffusion degree at $N=50$. This is because the larger-scale cluster environment has a lower sensitivity to sales price compared with the smaller-scale cluster environment due to its own larger volume. From this, it can be concluded that the selling price of enterprises’ low-carbon products can have an impact on the diffusion of low-carbon technological co-innovation results within the cluster environment, but it is not a sufficient condition to improve the diffusion efficiency.

4.6. Robustness Analysis of Key Parameters

Figure 11 and Figure 12 represent the impact of the diffusion of cooperation results of $p_n$ under different values of $\sigma$.

To verify the model’s stability (i.e., the impact of changes in relevant parameters on the evolutionary trajectory when $\sigma$ varies). If $\sigma$ changes, all the simulation graphs of the previous variables ($\gamma$, $\beta$, $\theta$, $\alpha$, $p_n$) in the entire paper will undergo some changes, although these changes will not affect their ultimate evolutionary trend. Therefore, we simulated the evolution trend of $p_n$ in ${\sigma }^{\prime }s$ variation from 0.05 to 0.20. Comparing Figure 11 and Figure 12 reveals that variations in $\sigma$ only induce minor shifts in the evolutionary trajectory without altering its ultimate evolutionary trend. Therefore, this finding demonstrates the stability of the preceding results.

The study carried out by Ge et al. [46] brilliantly unveils the macro-level panorama of China’s innovation ecosystem, revealing notable spatial clustering tendencies, a “core-periphery” structure, and community characteristics driven by technological connections rather than strict geographical proximity. These findings provide a robust factual foundation for understanding the static structure of industrial clusters. However, analyses based on historical association data not to illuminate the micro-level dynamic mechanisms underpinning these macro-structures—namely, the decision-making rules by which enterprises select partners, and how new innovation paradigms such as low-carbon technologies diffuse within these observed network structures. To address this question, our research employs complex network evolutionary game theory models. We no longer treat network structures as a given static backdrop, but rather as the stage for strategic interactions between enterprises.

The study carried out by Stoenoiu C.E. and Jantschi L. [61] provided a valuable macroeconomic perspective on the sustainable development of non-financial enterprises across Eastern Europe. In contrast to their research, our study introduces a complex network evolutionary game model. This methodology allows us to move beyond identifying what factors matter, to simulating how they dynamically influence the diffusion of low-carbon technologies through mimicry, competition, and collaboration between connected enterprises. By focusing on the industrial cluster environment, we argue that this model offers a nuanced and mechanistic understanding of the speed and pathways of corporate green innovation adoption.

The study by Ma et al. [62] compellingly demonstrates that macro-environmental threats constitute the pivotal external driver of green innovation transformation at the national level. However, this macro-level perspective struggles to illuminate the intrinsic micro-dynamic mechanisms within the transformation process—particularly within tightly interconnected ecosystems such as industrial clusters—where technological diffusion is realized through strategic interactions between enterprises. Therefore, this paper shifts its analytical focus from the national level to the internal dynamics of industrial clusters. Employing a complex network evolutionary game model, we aim to demonstrate that it is not external environmental pressures, but rather the interplay between internal network structures and game-theoretic payoffs that jointly determine the pace at which enterprises adopt low-carbon technologies.

5. Conclusions

This paper utilizes the complex network evolutionary game model to conduct an in-depth study on the diffusion process of low-carbon technology co-innovation cooperation results of enterprises as well as the micro changes of enterprise strategy selection in the cluster environment. And based on the results of numerical simulation, this paper discusses in depth the influence of relevant factors on the effectiveness of the diffusion of low-carbon technology collaborative innovation results within the cluster environment. Based on the analysis, we got some interesting results.

For each cooperative enterprise participating in low-carbon technology co-innovation, increasing the purchase subsidies for enterprises to purchase low-carbon production equipment can increase the diffusion rate of low-carbon technology co-innovation results, but the specific amount of purchase subsidies cannot be generalized. The larger network size of the cluster environment, the more low-carbon production equipment purchase subsidies will be required. This finding is consistent with the previous view that reducing the cost of clean energy and associated equipment will promote its widespread adoption [57], but reinforces the point that industrial clusters of varying network sizes have differing subsidy requirements.

Increasing the carbon emission tax rate of enterprises can also improve the diffusion rate of low-carbon technology collaborative innovation achievements by restraining the business behavior of enterprises, but the different scales of cluster environments will lead to different tolerances of enterprises to the carbon emission tax rate. Therefore, the relevant government departments need to formulate a reasonable and effective carbon emission tax rate after comprehensive research and assessment.

Carbon tax incentives are not necessarily effective for the diffusion of low-carbon technology co-innovation cooperation results among enterprises in cluster environments, and larger cluster environments are not sensitive to changes in carbon tax incentives.

Increasing the level of cluster management, specialization and characterization and thus improving the conversion rate of low-carbon ecological construction in the cluster environment can promote the diffusion of low-carbon technological collaborative innovation achievements, especially in the cluster environment with a large network scale, which has a higher requirement for the conversion rate of low-carbon ecological construction. In addition, it can be found that findings 2, 3, and 4 are consistent with the previous view that the government must intervene in accordance with the specific characteristics of industrial networks [61]. However, it is worth noting that our research more directly indicates that governments should adopt differentiated policies for industrial clusters of varying network sizes, namely for small-scale clusters, carbon taxes and subsidy-related policies can be employed to promote the diffusion of low-carbon technologies; whereas for large-scale clusters, efforts should focus on fostering the development of low-carbon ecosystems to facilitate such diffusion.

Reasonable changes in the selling price of low-carbon products can also have an impact on the diffusion of the results of collaborative innovation cooperation in low-carbon technologies among enterprises in cluster environments, but it is not a sufficient condition to improve the diffusion efficiency of innovation results, and larger cluster environments are not sensitive to changes in the selling price of products. In contrast to Zeng’s view that consumers’ environmental attitudes positively promote the dissemination of low-carbon technologies [59], this paper focuses on the influence of price factors. Given that consumers represent the final stage in the product value chain, price constitutes a key constraint influencing their purchasing decisions. Therefore, this research thereby reveals the role of price mechanisms, offering a significant supplement to existing theory.

6. Practical Implication

Based on the conclusions of the above research, this paper puts forward corresponding suggestions and countermeasures on how to accelerate the diffusion efficiency of low-carbon technology co-innovation achievements in cluster environments. Specific suggestions and countermeasures are as follows.

Implement targeted interventions based on cluster scale. The most crucial policy implication of this study is that differentiated governance must be applied according to cluster size. For small-scale clusters, both carbon taxes and subsidies demonstrate high policy sensitivity. Decision-makers should adopt a combination strategy of ‘precision application’, simultaneously using subsidies to stimulate adoption willingness and carbon taxes to phase out outdated technologies, thereby rapidly disseminating low-carbon technological innovations. Conversely, for large-scale clusters exhibiting structural inertia, the policy focus should shift from economic incentives to systemic governance. Efforts should concentrate on improving information flow and strengthening coordination mechanisms to fundamentally reduce the coordination costs associated with the diffusion of low-carbon technological innovations.

Leading enterprises within cluster environments should proactively assume responsibility. The network game analysis in this paper indicates that the diffusion of low-carbon technologies is a process driven by interactions and strategic choices of enterprises. Therefore, enterprises—particularly leading enterprises within cluster environments—should proactively assume the role of “diffusion catalysts”, transforming low-carbon transition from a compliance cost into a competitive advantage. Leveraging their network centrality, they can spearhead the establishment of low-carbon technology sharing platforms, industrial alliances, or joint innovation centers. By providing technical consultancy, certification services, or even sharing intellectual property with SMEs within the cluster, they can significantly reduce SMEs’ information search costs and technological barriers, thereby overcoming the dilemma of “hesitation to transition and lack of know-how to transition”.

Identify the value and strengths of the results and develop a targeted outreach strategy. In the cluster environment, after the enterprises’ low-carbon technology collaborative innovation produces new cooperative results; first of all, it needs to deeply understand the functions, characteristics and application fields of the cooperative results, and then make clear how the cooperative results can help the relevant enterprises to reduce the production cost, enhance the production efficiency, improve the quality of products and improve the competitiveness of the market. Subsequently, targeted promotion strategies should be formulated according to the specific characteristics of the cooperation results. Industry associations, technology forums and information exchange platforms within the cluster environment can be fully utilized to enhance the influence and visibility of the cooperation results. Technical seminars can also be organized to enhance the recognition and understanding of other enterprises of the cooperation results through the demonstration of the leading enterprises.

A mechanism for technology transfer and diffusion should be established and continuously tracked and evaluated. Within the cluster environment, specialized technology transfer centers and promotion agencies should be set up to help other enterprises within the cluster environment to understand and apply the results of cooperation in low-carbon technology co-innovation through consultation, training and technology demonstration. In addition, it is also necessary to continuously track the diffusion of cooperation results in the cluster environment, regularly assess the effectiveness and problems of the diffusion of cooperation results, and then adjust and optimize the diffusion strategy in a timely manner. Meanwhile, the establishment of effective feedback channels to collect the opinions and suggestions of other enterprises within the cluster environment can also be an important reference for the continuous improvement of measures for the diffusion of the results of the low-carbon technology collaborative innovation cooperation.

Policy support should be utilized to strengthen supervision and management. In the process of diffusion of the results of collaborative innovation cooperation in low-carbon technologies by enterprises, full attention should be paid to the supportive policies of the national and local governments on the promotion of new technologies, and efforts should be made to obtain substantial concessions in terms of funds and taxes. Meanwhile, make full use of the policy orientation to guide more enterprises within the cluster environment to participate in the promotion and application of the results of the cooperation. In addition, the findings of this paper also point out that large-scale cluster environments are not sensitive to preferential policies in the process of diffusion of cooperation results. In contrast, increasing the level of cluster management, specialization and features can significantly improve the diffusion efficiency of cooperation results in large-scale cluster environments. Therefore, it is essential to set up a perfect supervision and management mechanism and regularly summarize the diffusion status of cooperation results.

7. Limitations of the Study and Future Research

This paper constructs a complex network evolutionary game model based on BA scale-free networks, providing theoretical insights into the micro-mechanisms governing the diffusion of low-carbon technological innovations within cluster environments. Despite the considerable effort expended by the authors, the study nevertheless exhibits the following limitations. Firstly, to focus on core mechanisms, this study employs the classical BA scale-free network to abstract the industrial cluster environment. Whilst this captures many features of the “core-periphery” structure found in clusters, real-world industrial networks may be more complex. Consequently, future models could incorporate more diverse network topologies, such as small-world networks and multi-layer dynamic networks, to enhance the model’s explanatory power in real-world contexts. Moreover, the core findings of this study are grounded in mathematical derivations and computer simulations, and have yet to be empirically validated using real-world industrial cluster data. Consequently, future research could utilize industry databases or government statistical data to construct panel data models, thereby quantitatively analyzing the relationship between network structural characteristics, enterprise attributes, and the diffusion rate of low-carbon technologies.