Diffusion of Low-Altitude UAV Technology in Sustainable Development: An Evolutionary Game on Complex Networks

Abstract

Low-altitude unmanned aerial vehicle (UAV) technology serves as a crucial pathway for developing a low-carbon circular economy and achieving the Sustainable Development Goals (SDGs). In order to achieve the diffusion of low-altitude UAV technology in sustainable development, a dynamic model of technology adoption decisions within enterprise clusters is constructed. This model is based on complex network evolutionary game theory. The present study investigates the mechanism through which government policies influence the diffusion of low-altitude UAV technology. The research findings indicate that government subsidy mechanisms and diffusion constraints play critical roles in the diffusion process of low-altitude UAV technology. Core Enterprises and Marginal Enterprises within clusters exhibit different responsiveness to subsidies, with Core Enterprises demonstrating higher sensitivity. The intensity of government subsidies is positively correlated with the diffusion rate of low-altitude UAV technology, while the penalty from constraints is negatively correlated with the diffusion rate. These findings establish a foundation for governments to devise pertinent subsidy mechanisms, establish and enhance the management system of the low-altitude economy, and cultivate a policy ecosystem conducive to the diffusion of low-altitude UAV technology, thereby propelling sustainable societal development.

1. Introduction

Climate change is widely regarded as one of the most significant challenges currently facing society. The primary driver of global temperature rise and reduced precipitation is greenhouse gas emissions, which have induced climatic anomalies that have become a focal point of widespread international concern [1]. As the concept of green development becomes more entrenched and the process of ecological civilization construction progresses, public awareness of environmental protection continues to intensify. The paradigm of environmental protection has undergone a transition, evolving from a domain primarily governed by the state to a matter of societal governance [2]. Against this backdrop, to pursue low-carbon sustainable development, many countries have implemented strict carbon taxes to reduce greenhouse gas emissions [3]. Numerous countries have integrated Low-Carbon Smart City (LCSC) initiatives into their urban planning frameworks, with the aim of promoting societal sustainable development through the integration of renewable energy, sustainable transportation systems, and green infrastructure [4]. Asian countries such as Japan and South Korea have also formulated smart city development strategies, with a focus on enhancing energy efficiency and integrating low-carbon technologies. These strategies encompass areas such as carbon emission reduction, clean energy production, and pollutant control [5].

The low-altitude economy is an emerging industrial form that is becoming a significant force driving global low-carbon transition and ecological environmental protection. Within this paradigm, the predominant industry of the low-altitude economy is characterized by the integration of low-altitude unmanned aerial vehicle (UAV) technology, which leverages its flexible and efficient technical characteristics. As a key sector of the low-altitude economy, the flexible and efficient nature of low-altitude UAV technology means it is widely used in various scenarios related to sustainable development. It plays a pivotal role in enhancing operational efficiency, reducing carbon emissions, accelerating the low-carbon transformation of traditional industries, and mitigating environmental pollution [6]. In logistics and distribution, for example, low-altitude UAV technology can improve traffic efficiency and reduce carbon emissions [7,8]. In terms of agricultural plant protection, it has improved crop productivity, optimized production costs for farmers, and made significant contributions to food security [9,10,11]. In the field of inspection and monitoring, low-altitude UAV technology can be used to monitor environmental changes, as well as pollutants in the atmosphere, oceans, and other media [12,13,14].

As a key driver of sustainable social development, low-altitude UAV technology has emerged as a new area in which enterprises are competing to deploy their strategies for a low-carbon transition. Relevant data indicate that the scale of China’s low-altitude economy exceeded 500 billion yuan in 2023, with a growth rate as high as 33.8%, and it is projected to surpass 1 trillion yuan by 2026 [15]. In response, governments at all levels have implemented a series of supportive policies aimed at fostering the diversified and sustainable growth of the low-altitude economy [16]. Despite achieving phased results in market expansion and policy support, the low-altitude UAV industry still faces constraining factors such as technological bottlenecks, lagging infrastructure, underdeveloped market systems, and an inadequate management framework, which severely hinder the widespread application and deep diffusion of the technology [17]. Therefore, exploring the diffusion mechanism of low-altitude UAV technology from the perspective of government policy guidance holds significant theoretical reference value and practical guiding significance in terms of promoting social sustainable development.

The extant research on low-altitude UAVs is chiefly concentrated on macroscopic analysis of policy and descriptive overviews of industrial development. This has led to a homogeneity in policy studies, while critical gaps remain regarding the empirical impact of government subsidy schemes on technology diffusion and the tangible effects of development constraints—such as airspace governance, public acceptance, and safety concerns—on enterprise decision-making behaviour. Although prior studies have established the theoretical necessity of supportive policies and highlighted the importance of addressing constraints, they lack a nuanced, empirical analysis that accounts for the heterogeneity among enterprises operating at differing technological maturity levels [18,19,20]. Consequently, there is a conspicuous absence of a dynamic simulation model that integrates these multifaceted factors to accurately trace diffusion pathways.

This gap is particularly pressing given the urgent need to align technological advancement with SDGs. The adoption of low-altitude UAVs promises significant contributions to sustainability. However, without a realistic model that incorporates diverse enterprise behaviors, policy incentives, and real-world constraints, policymakers lack the tools to effectively steer this diffusion toward maximizing its sustainable outcomes. Therefore, this study employs a complex network evolutionary game model framework to introduce government subsidy mechanisms and development constraints with a view to systematically analysing the diffusion process of low-altitude UAV technology in sustainable development applications. The objective of this study is to elucidate the mechanism of government policy on technology diffusion. Compared with traditional evolutionary game models, the complex network evolutionary game model used in this study has distinct advantages: on the one hand, traditional game models struggle to capture the impacts of heterogeneous connections and asymmetric interactions among enterprises, whereas complex network models can better simulate the social network effects of technology diffusion in the real world; on the other hand, the diffusion of low-altitude UAV technology itself exhibits obvious network characteristics and geographical constraints, and the complex network method is particularly suitable for analyzing the diffusion mechanism of such technologies within specific network structures. This method fills the gap in the field of low-altitude UAV technology diffusion modeling and provides a theoretical reference for improving diffusion efficiency and enriching modeling practices in sustainable development research. The potential innovations of this paper include:

(1)

The complex network evolutionary game model is to be migrated to the study of low-altitude UAV diffusion.

(2)

Multiple factors affecting enterprise profit decision-making are to be comprehensively considered.

(3)

Traditional game theory analysis results are to be compared with complex network simulation results in order to verify the rationality of the model and parameter values.

2. Literature Review

2.1. Technology Diffusion Theory and Low-Attitude UAV Development

Technology diffusion is a critical process driving economic and technological advancement. It refers to the mechanism by which adopters introduce new technologies from innovation sources to enhance technical efficiency, narrow technological gaps, and achieve continuous innovation through the digestion and absorption of knowledge [21]. This process exhibits socioeconomic attributes: its cost-effectiveness is reflected in how technological progress boosts productivity and reduces product prices, thereby fostering denser production networks and further accelerating technology propagation [22]. When a limited number of enterprises pioneer the adoption of new technology and reap excess profits, it creates a profit incentive that drives imitation and broader market uptake [23]. To further investigate technology diffusion behavior, academia has developed a series of theories. The Diffusion of Innovations Theory focuses on the process of innovation propagation within social systems [24]. Schumpeter and Pavitt proposed that a technology or concept can be regarded as an innovation if it possesses five characteristics: compatibility, relative advantage, trialability, complexity, and observability [25,26]. This theory has been widely applied across various fields: in low-carbon technology, Yang et al. established a mathematical model of the interaction between clean technology dissemination and interregional coordinated behavior [27]. Wang et al. developed a diffusion model for photovoltaic power generation technology by studying the dynamic effects of individual behavioral interactions [28]. In digital technology, Zhou et al. provided a comprehensive analysis of the development trends of digital technology in China, offering important insights for policymakers [29]. Blaettchen et al. revealed the impact of supply chain network structures on technology diffusion through large-scale numerical experiments [30]. In the construction field, Pan et al. studied the diffusion of green building practices, providing valuable references for policy formulation in industrial clusters [31].

It is evident that low-altitude UAV technology possesses these five innovation characteristics, laying the groundwork for applying the Diffusion of Innovations Theory. As a strategic emerging industry, low-altitude UAV research has formed a systematic framework guided by development strategies, supported by key technologies, and centered on application scenarios. However, existing studies lack dynamic diffusion models that integrate multiple factors. Current UAV research can be divided into two main directions: The first is regulatory policy research. Guo studied the classified supervision and legal regulation of UAVs from the perspective of low-altitude intelligent connectivity, proposing the establishment of an inclusive and prudent regulatory concept and the improvement of real-time regulatory measures [32]. Liao analyzed the mismatch between China’s UAV regulatory system and the demands of the low-altitude economy, drawing on U.S. experience to propose a concept of “simultaneously advancing safety assurance and innovation promotion” [33]. Zhou systematically explored the application models, technical design, and policy challenges of UAVs in sustainable smart cities. The second is application scenario exploration [34]. Ozbiltekin-Pala et al. investigated the application of UAVs in emergency logistics, providing a theoretical basis for optimizing their use in this field [35]. Vishal systematically analyzed the application of UAVs and low-cost sensors in air quality monitoring [36]. Sadrabadi et al. proposed a conceptual design for a UAV swarm-enabled wildfire emergency response system based on a systems engineering approach [37]. Zhang et al. explored the reasons for urban residents’ low acceptance of normalized UAV delivery, developing more reasonable management solutions [38].

2.2. Complex Network Evolutionary Game

Evolutionary game theory is predicated on traditional game theory and biological evolution, with its focus being on the interactive relationships between individuals and the strategy adjustment mechanisms of decision-makers in dynamic processes. This theory seeks to provide a scientific theoretical framework for the study of dynamic processes of development [39]. Per co-evolution theory, stakeholders’ decisions are both the consequence of other entities’ actions in the system and a reaction to them [40]. In the contemporary era, interactions and evolution among entities are becoming increasingly frequent. In the course of the exchange of information, entities undertake a comparison of their payoffs with those of their neighbors. This process of comparison enables them to learn to imitate the behaviour of their neighbors. The result of this is that the decisions of the neighbors diffuse within the system, thereby forming a social multiplier effect [41]. It is evident that the complex network method, which is utilised to investigate the topological network characteristics and statistical features within systems, is employed in the study of complex interaction mechanisms of agents based on evolutionary game models [42]. A significant number of scholars employ complex network evolutionary game models to describe the dynamic adjustment process of entities within a system and to reveal key factors influencing diffusion and their mechanisms. In the field of low-carbon technology diffusion, Li et al. employed a complex network evolutionary game approach to explore the dynamic impact of government policies on electric vehicle diffusion in networks of different sizes [43]. In consideration of the heterogeneity of consumer groups and construction enterprises, Yang et al. employed a complex network evolutionary game model to investigate the evolutionary patterns of green transformation in construction enterprises [44]. Li et al. constructed an evolutionary game model for the innovation and diffusion of green energy technology in a complex network environment, focused on analysing the impact of multiple key parameters on the equilibrium results of evolutionary strategies [45]. Pan et al. explored the diffusion of CCUS technology in the coal-to-hydrogen sector against the backdrop of carbon trading market dynamics [46]. In their seminal study, Zheng et al. employed a multi-faceted network evolutionary game approach to reveal the complex dynamics of green technology diffusion [47]. It is evident that the utilisation of the complex network evolutionary game method in the study of group evolution, concerning structure and function, is conducive to the acquisition of certain theoretical advantages. Furthermore, this method is highly suitable for the research of sustainable development technology diffusion.

A review of the extant literature indicates that the study of the diffusion of low-altitude UAV technology using the complex network evolutionary game approach has a solid theoretical foundation and is a necessary research endeavor. This theoretical framework provides a foundation for governments seeking to optimise the layout of the low-altitude UAV industry and promote sustainable social development. The present paper employs a complex network evolutionary game model to simulate the dynamic interactions between government policy interventions and corporate decision-making behaviors in the diffusion of low-altitude UAV technology. The model construction involves the following steps: First, enterprise clusters are categorized into Core Enterprises A and Marginal Enterprises B, representing entities with differing levels of technological application maturity. Second, profit functions for enterprises are established, incorporating multiple influencing factors such as government subsidies, technological maturity, and market preferences. Third, the replicator dynamic equations are used to analyze the evolutionarily stable strategies (ESS) of the system. Finally, an enterprise interaction network is constructed based on the NW small-world network, and the Fermi rule is adopted to simulate the strategy update process among enterprises. Numerical simulations are conducted using MATLAB R2024a to examine the impact of factors such as government subsidy intensity and constraint penalties on the technology diffusion rate, thereby providing theoretical support for the scientific decision-making processes of governments and enterprises.

3. Game Model Construction

3.1. Model Assumptions

The present study examines a three-tier supply chain comprising manufacturers, enterprise groups, and consumers. The total number of enterprises included in the group is represented by the variable $N$. These $N$ enterprises can be categorised into two distinct types, Core Enterprise A and Marginal Enterprise B are distinguished by disparate maturity of low-altitude UAV technology applications. It is evident that both parties have the capacity to engage in sustainable innovation by adopting low-altitude UAV technology, or alternatively, they may elect to maintain their current production and operation by utilizing traditional technology without undergoing any modifications.

Assumption 1. 

The diffusion of low-altitude UAV technology is defined as the process of its dissemination and application promotion across different fields, regions, and user groups. In this process, each enterprise in the cluster is faced with two possible options for sustainable development: namely, the adoption of low-altitude UAV technology or traditional technology. The proportion of enterprises adopting low-altitude UAV technology among the $N$ enterprises is represented by $q$, where the proportions of Core Enterprise A and Marginal Enterprise B are $x$ and $y$, respectively $\left(x,y\in \left[\mathrm{1,0}\right]\right)$.

Assumption 2. 

It is assumed that the total market demand is $Q=2\alpha$. Consumer preference for low-altitude UAV technology is represented by the parameter $\lambda$. This parameter is defined as the inclination exhibited by user groups when selecting and applying low-altitude UAV technology, influenced by concepts such as low-carbon and sustainable development. In the event of one enterprise in the cluster adopting low-altitude UAV technology and the other adopting traditional technology, the adopting enterprise gains an additional market share, denoted by $\lambda$, while the non-adopting enterprise loses market share, also denoted by $\lambda$. Conversely, if both enterprises adopt low-altitude UAV technology or both adopt traditional technology, their market shares are both $\alpha$.

Assumption 3. 

It is assumed that the cost for an enterprise utilizing traditional technology is represented by $c_{t }$ and that the cost for enterprises employing low-altitude UAV technology is denoted by $c_l$. It is posited that mature low-altitude technology has the capacity to optimise service and product performance, thereby increasing enterprise revenue. It is further hypothesized that the maturity in the application of low-altitude UAV technology, ${\tau }_i\left({\tau }_i>0,i=A,B\right)$, exerts a non-linear decreasing characteristic on the cost of low-altitude UAV. This is illustrated by the following equation: $c_l{e}^{-{\tau }_i}$. Presently, the low-altitude economy is still in its nascent stage of development and is subject to numerous constraints, including safety risks, airspace restrictions, and imperfect infrastructure. These factors impose a “penalty for diffusion constraints” on enterprises that adopt low-altitude UAVs. Therefore, it can be assumed that the penalty for low-altitude UAV diffusion constraints is $c$.

Assumption 4. 

Low-altitude UAV technology diffusion is a process led by the government and involving collaboration between enterprises. Whether or not enterprises can take the lead depends crucially on government policy support and guidance. To promote the development of the low-altitude UAV industry and social sustainability during its diffusion process, the government provides subsidies $s$ to enterprises that adopt UAV technology.

Assumption 5. 

During the development of low-altitude UAV technology, the government may choose to subsidize low-altitude UAV manufacturers, thereby increasing their R&D investment and promoting the development level of low-altitude UAV technology. Assuming the government’s subsidy intensity for low-altitude UAV manufacturers is $v$, government subsidies can accelerate the development level of low-altitude UAV technology, thereby promote enterprises to achieve greater maturity in the application of low-altitude UAV technology, expressed as ${\tau }_i={\tau }_{i0}+\beta v$, where ${\tau }_{i0}>0$ is the initial maturity of low-altitude UAV technology applications, and $\beta >0$ is the impact coefficient of government subsidies on the development level of low-altitude UAV technology.

Assumption 6. 

Consumers use traditional technology services to meet general demand. Enterprises that provide these services obtain a perceived value benefit $w>0$. When enterprises use low-altitude UAV technology to serve consumers, they generate an additional perceived value benefit $∆w$. This includes the additional perceived value benefit that consumers gain from the efficiency, sustainability, convenience, and other multiple values added by low-altitude UAV technology. The incremental perceived value benefit $∆w$ is positively correlated with the maturity of low-altitude UAV technology applications, ${\tau }_i$. The prices paid by consumers for traditional technology services and low-altitude UAV technology services are $p^t$ and $p^l$, respectively.

The mathematical notation used in this paper is summarized in

Table 1. Parameter Definitions.

Symbol	Meaning
$c_{\mathrm{t}}$	Operating cost for enterprises using traditional technology
$c_{\mathrm{l}}$	Operating cost for enterprises using low-altitude UAV technology
$c$	Penalty for low-altitude UAV diffusion constraints
$N$	The number of enterprises in the network
$p^t$	Price paid by consumers for traditional technology services
$p^l$	Price paid by consumers for low-altitude technology services
$Q$	Total market demand
$q$	Proportion of enterprises adopting low-altitude UAV technology in the cluster
$s$	Subsidy given by the government to enterprises adopting low-altitude UAVs
$v$	Government subsidy intensity for low-altitude UAV manufacturers
$w$	Perceived value benefit of consumers for traditional technology
$∆w$	Perceived value benefit of consumers for low-altitude UAV technology
$\lambda$	Consumer preference for low-altitude UAV technology
${\tau }_i$	Maturity of low-altitude UAV technology applications
${\tau }_{i0}$	Initial maturity of low-altitude UAV technology applications
$\alpha$	The respective market shares of Core Enterprises and Marginal Enterprises when they adopt the same strategy
$\beta$	Impact coefficient of government subsidies on the development level of low-altitude UAV technology
${\pi }_i^l$	The profits for Enterprises adopting low-altitude UAV technologies
${\pi }_i^t$	The profits for Enterprises adopting traditional technologies

.

3.2. Enterprise Profits Under Government Intervention

The profits for Core Enterprise A and Marginal Enterprise B in the cluster adopting low-altitude UAV and traditional technologies are ${\pi }_A^l$,${\pi }_B^l, {\pi }_A^t \mathrm{a}\mathrm{n}\mathrm{d} {\pi }_B^t$, respectively. Accordingly, the game payoff matrix for Core Enterprise A and Marginal Enterprise B under different strategies is shown in

Table 2. Payoff Matrix for Core Enterprise A and Marginal Enterprise B.

Marginal Enterprise B	Core Enterprise A
	Low-Altitude UAV Technology $\left(\mathit{x}\right)$	Traditional Technology $(1-\mathit{x})$
Low-altitude UAV Technology $\left(y\right)$	${\pi }_A^{ll}$; ${\pi }_B^{ll}$	${\pi }_A^{lt}$; ${\pi }_B^{lt}$
Traditional Technology $(1-y)$	${\pi }_A^{tl}$; ${\pi }_B^{tl}$	${\pi }_A^{tt}$; ${\pi }_B^{tt}$

.

• where:

  $$\begin{array}{c}{\pi }_A^{ll}=\alpha \left[p^l-c_l{e}^{-{\tau }_A}+∆w{\tau }_A+s-c\right]\end{array}$$

  (1)

  $$\begin{array}{c}{\pi }_B^{ll}=\alpha \left[p^l-c_l{e}^{-{\tau }_B}+∆w{\tau }_B+s-c\right]\end{array}$$

  (2)

  $$\begin{array}{c}{\pi }_A^{lt}=\left(\alpha +\lambda \right)\left[p^l-c_l{e}^{-{\tau }_A}+∆w{\tau }_A+s-c\right]\end{array}$$

  (3)

  $$\begin{array}{c}{\pi }_B^{tl}=\left(\alpha -\lambda \right)\left(p^t-c_t+w\right)\end{array}$$

  (4)

  $$\begin{array}{c}{\pi }_A^{tl}=\left(\alpha -\lambda \right)\left(p^t-c_t+w\right)\end{array}$$

  (5)

  $$\begin{array}{c}{\pi }_B^{lt}=\left(\alpha +\lambda \right)\left[p^l-c_l{e}^{-{\tau }_B}+∆w{\tau }_B+s-c\right]\end{array}$$

  (6)

  $$\begin{array}{c}{\pi }_A^{tt}=\alpha \left(p^t-c_t+w\right)\end{array}$$

  (7)

  $$\begin{array}{c}{\pi }_B^{tt}=\alpha \left(p^t-c_t+w\right)\end{array}$$

  (8)

The expected profit for Core Enterprise A adopting low-altitude UAV technology is:

$$\begin{array}{c}{E}_A^l=y{\pi }_A^{ll}+\left(1-y\right){\pi }_A^{lt}=\left[\alpha +\lambda \left(1-y\right)\right]\left[p^l-c_l{e}^{-{\tau }_A}+∆w{\tau }_A+s-c\right]\end{array}$$

(9)

The expected profit for Core Enterprise A adopting traditional technology is:

$$\begin{array}{c}{E}_A^t=y{\pi }_A^{tl}+\left(1-y\right){\pi }_A^{tt}=\left(p^t-c_t+w\right)\left(\alpha -y\lambda \right)\end{array}$$

(10)

The average expected profit for Core Enterprise A adopting low-altitude UAV technology and traditional technology is:

$$\begin{array}{c}\overline{E_A}=x{E}_A^l+\left(1-x\right)E_A^t\end{array}$$

(11)

The expected profit for Marginal Enterprise B adopting low-altitude UAV technology is:

$$\begin{array}{c}{E}_B^l=x{\pi }_B^{ll}+\left(1-x\right){\pi }_B^{lt}=\left[\alpha +\lambda \left(1-x\right)\right]\left[p^l-c_l{e}^{-{\tau }_B}+∆w{\tau }_B+s-c\right]\end{array}$$

(12)

The expected profit for Marginal Enterprise B adopting traditional technology is:

$$\begin{array}{c}{E}_B^t=x{\pi }_B^{tl}+\left(1-x\right){\pi }_B^{tt}=\left(p^t-c_t+w\right)\left(\alpha -x\lambda \right)\end{array}$$

(13)

The average expected profit for Marginal Enterprise B adopting low-altitude UAV technology and traditional technology is:

$$\begin{array}{c}\overline{E_B}=y{E}_B^l+\left(1-y\right)E_B^t\end{array}$$

(14)

Based on the above payoff matrix, the replicator dynamic equations for Core Enterprise A and Marginal Enterprise B are as follows:

$$\begin{array}{c}F\left(x\right)={\displaystyle \frac{dx}{dt}}=x\left(1-x\right)\left(E_A^l-E_A^t\right)\end{array}$$

(15)

$$\begin{array}{c}F\left(y\right)={\displaystyle \frac{dy}{dt}}=y\left(1-y\right)\left(E_B^l-E_B^t\right)\end{array}$$

(16)

To simplify the calculations, make the following assumptions: $R_i=p^l-c_l{e}^{-{\tau }_i}+∆w{\tau }_i+s-c$, representing the profit of enterprise $i(i=A,B)$ when adopting low-altitude UAV technology. $D_i=R_i-(p^t-c_t+w)$, representing the profit difference between adopting low-altitude UAV technology and traditional technology.

3.3. Evolutionary Stability Analysis

A decision dynamic evolution system is constructed based on the replicator dynamic equations of Core Enterprise A and Marginal Enterprise B in the cluster. Let $F\left(x\right)=0 and F\left(y\right)=0$, yielding 5 system equilibrium points: $E_1\left(\mathrm{0,0}\right),E_2\left(\mathrm{1,1}\right),E_3\left(\mathrm{1,0}\right),{ E}_4\left(\mathrm{0,1}\right) \mathrm{a}\mathrm{n}\mathrm{d} E_5\left(x^{\mathrm{*}},y^{\mathrm{*}}\right),$ where: $x^{\mathrm{*}}={\displaystyle \frac{\alpha D_B+\lambda R_B}{\lambda D_B}}{,y}^{\mathrm{*}}={\displaystyle \frac{\alpha D_A+\lambda R_A}{\lambda D_A}}$.

The evolutionary stable strategy (ESS) is determined based on the asymptotic stability conditions for evolutionary games. An equilibrium point that satisfies the condition that the determinant of the Jacobian matrix is greater than zero $\left(det>0\right)$ and its trace is less than zero $(tr<0)$ is an ESS of the game system. The Jacobian matrix of the dynamic evolution system for an enterprise cluster adopting the low-altitude UAV technology strategy is as follows:

$$J=\left[\begin{array}{cc}{\displaystyle \frac{\partial F\left(x\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(x\right)}{\partial y}}\\ {\displaystyle \frac{\partial F\left(y\right)}{\partial x}}& {\displaystyle \frac{\partial F\left(y\right)}{\partial y}}\end{array}\right]=\left[\begin{array}{cc}{J}_{11}& J_{12}\\ J_{21}& J_{22}\end{array}\right]$$

(17)

The calculations yield the following: $J_{11}=\left(1-2x\right)\left[\alpha D_A+\lambda \left(R_A-y{D}_A\right)\right];J_{12}=-\lambda D_{A}x\left(1-x\right);J_{21}=-\lambda D_{B}y\left(1-y\right);J_{22}=\left(1-2y\right)[\alpha D_B+\lambda (R_B-x{D}_B\left)\right]$.

According to the formula for the Jacobian matrix solution and the judgment method, the equilibrium point for the dynamic evolution of the enterprise group’s decision-making is obtained when $\det \left(J\right)=J_{11}{J}_{22}>0 \mathrm{a}\mathrm{n}\mathrm{d} tr\left(J\right)=J_{11}+J_{22}<0$ are simultaneously satisfied. The values of the determinant and trace of the Jacobian matrix at different equilibrium points are calculated as shown in

Table 3. Determinant and Trace Values of the Jacobian Matrix at Equilibrium Points.

Equilibrium Points	$\mathbf{det}\left(\mathit{J}\right)$	$\mathit{t}\mathit{r}\left(\mathit{J}\right)$
$E_1\left(\mathrm{1,1}\right)$	$\left[\alpha D_A+\lambda \left(p^t-c_t+w\right)\right]$ $[\alpha D_B+\lambda \left(p^t-c_t+w\right)]$	$-[\alpha D_A+\lambda \left(p^t-c_t+w\right)$ $+\alpha D_B+\lambda \left(p^t-c_t+w\right)]$
$E_2\left(\mathrm{0,1}\right)$	$-[\alpha D_A+\lambda \left(p^t-c_t+w\right)](\alpha D_B+\lambda R_B)$	$\left[\alpha D_A+\lambda \left(p^t-c_t+w\right)\right]$ $-(\alpha D_B+\lambda R_B)$
$E_3\left(\mathrm{1,0}\right)$	$-(\alpha D_A+\lambda R_A)[\alpha D_B+\lambda \left(p^t-c_t+w\right)]$	$-\left(\alpha D_A+\lambda R_A\right)+$ $[\alpha D_B+\lambda \left(p^t-c_t+w\right)]$
$E_4\left(\mathrm{0,0}\right)$	$(\alpha D_A+\lambda R_A)(\alpha D_B+\lambda R_B$)	$\left(\alpha D_A+\lambda R_A\right)+(\alpha D_B+\lambda R_B$)
$E_5(x^{*},y^{*})$	${-\lambda }^2{D}_A{D}_B{x}^{*}(1-x^{*})y^{*}(1-y^{*})$	0

.

According to Table 3, when the stable point is $(x^{*},y^{*})$, it does not satisfy the above judgment conditions, i.e., $\mathit{det}\left(J\right)<0 \mathrm{a}\mathrm{n}\mathrm{d} tr\left(J\right)=0$. Therefore, this point is not an evolutionarily stable strategy (ESS). Further analysis of the signs of $\det \left(J\right)$ and $tr\left(J\right)$ can be used to determine the stability of each equilibrium point and the conditions under which it is stable. The following propositions can be derived from this analysis:

Proposition 1. 

The intensity of the government subsidies $s$ for enterprises adopting low-altitude UAV technology influences the stability of the cluster enterprises’ decisions to adopt the technology. During the system’s dynamic evolution, the two types of enterprise have different expected subsidy thresholds, causing core and Marginal Enterprises to adopt different evolutionary strategies at various stages. The ESS of the system differs when government subsidies fall within different threshold intervals. Specifically, there are five scenarios:

When $s>max\{s_{A2},s_{B2}\}$, both Core Enterprise A and Marginal Enterprise B adopt low-altitude UAV technology.

When $0<s<s_{A1} and{ s}_{B1}<s<s_{B2}$, Core Enterprise A does not adopt low-altitude UAV technology, while Marginal Enterprise B adopts it.

When $s_{A1}<s<s_{A2} and 0<s<s_{B1}$, only Core Enterprise A adopts low-altitude UAV technology.

When $s<min\{s_{A1},s_{B1}\}$, both enterprises abandon the adoption of low-altitude UAV technology.

When $s_{A1}<s<s_{A2}{ and s}_{B1}<s<s_{B2},$ compared to scenario 4, the government subsidy $s$ has increased but has not yet reached the level of scenario 1. The system may exhibit two different stable states. As shown in Figure 1e, the final evolutionary outcome of the system is influenced by the parameters $(x^{*},y^{*})$. The greater the area of quadrilateral BCDE, the higher the probability that enterprises in the cluster will adopt low-altitude UAV technology. Where:

$$s_{A1}=-{\displaystyle \frac{-\left(\alpha +\lambda \right)\left[p^l-c_l{e}^{-{\tau }_A}+∆w{\tau }_A-c\right]+\alpha \left(p^t-c_t+w\right)}{\alpha +\lambda }}$$

$$s_{A2}={\displaystyle \frac{-\alpha \left[p^l-c_l{e}^{-{\tau }_A}+∆w{\tau }_A-c\right]-(\lambda -\alpha )\left(p^t-c_t+w\right)}{\alpha }}$$

$$s_{B1}=-{\displaystyle \frac{-\left(\alpha +\lambda \right)\left[p^l-c_l{e}^{-{\tau }_B}+∆w{\tau }_B-c\right]+\alpha \left(p^t-c_t+w\right)}{\alpha +\lambda }}$$

$$s_{B2}={\displaystyle \frac{-\alpha \left[p^l-c_l{e}^{-{\tau }_B}+∆w{\tau }_B-c\right]-(\lambda -\alpha )\left(p^t-c_t+w\right)}{\alpha }}$$

Proof of Proposition 1. 

When government subsidies to enterprises in the cluster fall within different ranges, they affect the decision stability of game agents’ decisions. The proof process is shown in

Table 4. Stability Analysis of Enterprise Game System Equilibrium Points under Different Subsidy Levels.

Condition	Equilibrium Points	$\mathbf{det}\left(\mathit{J}\right)$	$\mathit{t}\mathit{r}\left(\mathit{J}\right)$	Stability
$s>\mathrm{m}\mathrm{a}\mathrm{x}\{s_{A2},s_{B2}\}$	$E_1\left(\mathrm{1,1}\right)$	+	−	ESS
	$E_2\left(\mathrm{0,1}\right)$	−	*	Saddle Point
	$E_3\left(\mathrm{1,0}\right)$	−	*	Saddle Point
	$E_4\left(\mathrm{0,0}\right)$	+	+	Unstable Point
	$E_5(x^{\mathrm{*}},y^{\mathrm{*}})$	−	0	Non-Equilibrium Point
$0<s<s_{A1},$ $s_{B1}<s<s_{B2}$	$E_1\left(\mathrm{1,1}\right)$	−	*	Saddle Point
	$E_2\left(\mathrm{0,1}\right)$	+	−	ESS
	$E_3\left(\mathrm{1,0}\right)$	+	+	Unstable Point
	$E_4\left(\mathrm{0,0}\right)$	−	*	Saddle Point
	$E_5(x^{\mathrm{*}},y^{\mathrm{*}})$	−	0	Non-Equilibrium Point
${\mathrm{s}}_{A1}<s<s_{A2,}$ $0<s<s_{B1}$	$E_1\left(\mathrm{1,1}\right)$	−	*	Saddle Point
	$E_2\left(\mathrm{0,1}\right)$	+	+	Unstable Point
	$E_3\left(\mathrm{1,0}\right)$	+	−	ESS
	$E_4\left(\mathrm{0,0}\right)$	−	*	Saddle Point
	$E_5(x^{\mathrm{*}},y^{\mathrm{*}})$	−	0	Non-Equilibrium Point
0$<s<s_{A1},$ $0<s<s_{B1}$	$E_1\left(\mathrm{1,1}\right)$	+	+	Unstable Point
	$E_2\left(\mathrm{0,1}\right)$	−	*	Saddle Point
	$E_3\left(\mathrm{1,0}\right)$	−	*	Saddle Point
	$E_4\left(\mathrm{0,0}\right)$	+	−	ESS
	$E_5(x^{\mathrm{*}},y^{\mathrm{*}})$	−	0	Non-Equilibrium Point
${\mathrm{s}}_{A1}<s<s_{A2},$ $s_{B1}<s<s_{B2}$	$E_1\left(\mathrm{1,1}\right)$	+	−	ESS
	$E_2\left(\mathrm{0,1}\right)$	+	+	Unstable Point
	$E_3\left(\mathrm{1,0}\right)$	+	+	Unstable Point
	$E_4\left(\mathrm{0,0}\right)$	+	−	ESS
	$E_5(x^{\mathrm{*}},y^{\mathrm{*}})$	−	0	Non-Equilibrium Point

Note: * denotes that the sign cannot be determined.

, and the system evolution phase diagrams under different subsidy levels are illustrated in Figure 1. □

In realistic scenarios, the level of development of low-altitude UAV technology at the Core Enterprise of the cluster is greater than at the Marginal Enterprise, i.e., ${\tau }_A>{\tau }_B$. Therefore, $s_{A1}>s_{B1}$. Consequently, the equilibrium point $E_3\left(\mathrm{1,0}\right)$ as the ESS of the game system lacks practical significance.

According to Figure 1e, the area of quadrilateral BCDE is given by: $S_{BCDE}=1-{\displaystyle \frac{1}{2}}({\displaystyle \frac{\alpha D_B+\lambda R_B}{\lambda D_B}}+{\displaystyle \frac{\alpha D_A+\lambda R_A}{\lambda D_A}})$. Considering that the increase or decrease of $S_{BCDE}$ depends on the increase or decrease of $x^{\mathrm{*}}+y^{\mathrm{*}}$, when $x^{\mathrm{*}}+y^{\mathrm{*}}\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{s},{ S}_{BCDE}$ increases, and the probability of enterprises adopting low-altitude UAV technology increases. Based on this, the following proposition is established:

Proposition 2. 

The probability of enterprises in the cluster adopting low-altitude UAV technology increases as the government’s subsidy intensity to low-altitude UAV manufacturers increases.

Proof of Proposition 2. 

Let $g_i={\displaystyle \frac{R_i}{D_i}}, \mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}:{ S}_{BCDE}=1-{\displaystyle \frac{\alpha }{\lambda }}-{\displaystyle \frac{1}{2}}(g_A+g_B)$

Since the government subsidies $v$ to low-altitude UAV manufacturers affect the maturity of low-altitude UAV technology applications ${\tau }_i$, which in turn affects $R_i and D_i$, first find ${\displaystyle \frac{\partial S_{BCDE}}{\partial {\tau }_i}}$, then use the chain rule to find ${\displaystyle \frac{\partial S_{BCDE}}{\partial v}}$.

$${\displaystyle \frac{\partial R_i}{\partial {\tau }_i}}=c_l{e}^{-{\tau }_A}+∆w,{\displaystyle \frac{\partial D_i}{\partial {\tau }_i}}=c_l{e}^{-{\tau }_A}+∆w$$

$${\displaystyle \frac{\partial g_i}{\partial {\tau }_i}}={\displaystyle \frac{\frac{\partial R_i}{\partial {\tau }_i}{D}_i-\frac{\partial D_i}{\partial {\tau }_i}{R}_i}{D_i^2}}=(c_l{e}^{-{\tau }_A}+∆w){\displaystyle \frac{D_i-R_i}{D_i^2}}$$

Since $p^t-c_t+w>0, \mathrm{i}\mathrm{t} \mathrm{f}\mathrm{o}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{s} \mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t} D_i-R_i=-(p^t-c_t+w)<0.$ Additionally, $c_l{e}^{-{\tau }_i}+∆w>0$, so ${\displaystyle \frac{\partial g_i}{\partial {\tau }_i}}<0$, and thus, ${\displaystyle \frac{\partial S_{BCDE}}{\partial {\tau }_i}}=-{\displaystyle \frac{1}{2}}{\displaystyle \frac{\partial g_i}{\partial {\tau }_i}}>0$.

Given ${\tau }_i={\tau }_{i0}+\beta v, \mathrm{w}\mathrm{e} \mathrm{h}\mathrm{a}\mathrm{v}\mathrm{e} {\displaystyle \frac{\partial {\tau }_i}{\partial v}}=\beta >0$.

Therefore:

$${\displaystyle \frac{\partial S_{BCDE}}{\partial v}}={\displaystyle \frac{\partial S_{BCDE}}{\partial {\tau }_A}}{\displaystyle \frac{\partial {\tau }_A}{\partial v}}+{\displaystyle \frac{\partial S_{BCDE}}{\partial {\tau }_B}}{\displaystyle \frac{\partial {\tau }_B}{\partial v}}=\beta ({\displaystyle \frac{\partial S_{BCDE}}{\partial {\tau }_A}}+{\displaystyle \frac{\partial S_{BCDE}}{\partial {\tau }_B}})$$

.

Because ${\displaystyle \frac{\partial S_{BCDE}}{\partial {\tau }_i}}>0$ and $\beta >0,{\displaystyle \frac{\partial S_{BCDE}}{\partial v}}>0, \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{t}\mathrm{h}\mathrm{u}\mathrm{s}, S_{BCDE}$ is an increasing function of $v$. An increase in the government’s subsidy intensity to manufacturers accelerates the maturity of low-altitude UAV technology applications, reducing enterprise operating costs and increasing benefits. This leads to a higher probability that the system evolves to (1, 1), thereby incentivizing enterprises to adopt low-altitude UAV technology. □

Proposition 3. 

A reduction in the penalty $c$, resulting from constraints on the development of low-altitude UAVs, will increase the likelihood of enterprises within the cluster adopting low-altitude UAV technology.

Proof of Proposition 3. 

Since

$${\displaystyle \frac{\partial R_i}{\partial c}}=-1,{\displaystyle \frac{\partial D_i}{\partial c}}={\displaystyle \frac{\partial }{\partial c}}[R_i-\left(p^t-c_t+w\right)={\displaystyle \frac{\partial R_i}{\partial c}}=-1$$

Then:

$${\displaystyle \frac{\partial }{\partial c}}\left({\displaystyle \frac{R_i}{D_i}}\right)={\displaystyle \frac{\frac{\partial R_i}{\partial c}{D}_i-\frac{\partial D_i}{\partial c}{R}_i}{D_i^2}}={\displaystyle \frac{(-1)D_i-(-1)R_i}{D_i^2}}={\displaystyle \frac{-D_i+R_i}{D_i^2}}$$

Let

$$T=p^t-c_t+w.$$

Then:

$${\displaystyle \frac{\partial S_{BCDE}}{\partial c}}=-{\displaystyle \frac{1}{2}}\left[{\displaystyle \frac{\partial }{\partial c}}\left({\displaystyle \frac{R_A}{D_A}}\right)+{\displaystyle \frac{\partial }{\partial c}}\left({\displaystyle \frac{R_B}{D_B}}\right)\right]=-{\displaystyle \frac{1}{2}}({\displaystyle \frac{T}{D_A^2}}+{\displaystyle \frac{T}{D_B^2}})$$

Since $T>0 \mathrm{a}\mathrm{n}\mathrm{d} D_i^2>0$, it follows that ${\displaystyle \frac{\partial S_{BCDE}}{\partial c}}<0$. Therefore, $S_{BCDE}$ is a decreasing function of $c$. As $c$ decreases, the area of quadrilateral BCDE increases, thereby increasing the probability that the system will evolve to (1, 1). Consequently, the probability that enterprises in the cluster will adopt low-altitude UAV technology increases. □

Although the evolutionary game model can describe the decision-making process involved in the adoption of low-altitude UAV technology among cluster enterprises, it still has limitations when it comes to fully capturing the complexity of interactions between enterprises and the differences between individuals. Complex network theory provides a more accurate perspective on capturing the interactive behaviors within a group. As the network structure changes, individual strategies also adjust accordingly [48]. Therefore, this paper will use complex network theory to analyse the evolutionary game model of enterprise adoption of low-altitude UAV technology, revealing the dynamic evolution mechanism in complex network environments.

4. Complex Network Model Construction

4.1. Construction of the Small-World Model

In network theory, market agents are interconnected and adapt symbiotically to each other in competition. Today, the connections between enterprises are closer and are characterized by the small-world feature of networks. In the initial state of a small-world network, each node is connected to its w nearest neighbours. The Watts-Strogatz (WS) small-world network then randomly disconnects and reconnects edges with a certain probability, which can disrupt the original connectivity. By contrast, the Newman–Watts (NW) small-world network enhances connectivity by randomly adding edges without altering the original relationships between nodes [49,50]. In previous studies, many scholars have used the NW small-world network to simulate the complex network relationships between enterprises. Hu et al. adopted the NW small-world network to explore the dynamic impacts of different policies on the popularization of electric vehicles [51]. Yang et al. analyzed the dynamic impacts of the proportion of digital subsidies and the influence of high-tech certification on the diffusion scope of enterprise digitalization, [52]. Therefore, the NW small-world network more accurately simulates the connection characteristics of enterprise networks. This paper uses the NW small-world network to construct a complex enterprise network ($G=(V,E)$), where $V=\left\{v_i\right\}$ represents the enterprise nodes in the network, and $e_n\in E$ represents the direct edge relationship between node enterprise $v_i$ and enterprise $v_j$. It is assumed that all connections in the network are undirected. If there is a connection between enterprise $i$ and $j, \mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n} (v_i,v_j)=1$, otherwise, $(v_i,v_j)=0$. The construction algorithm for the NW small-world network model is as follows:

(1)

Generate a nearest-neighbor coupled network with $N$ nodes arranged in a ring, where each node is connected to its $K$ nearest neighbors ($K$ is an even number). Randomly assign each enterprise an initial strategy based on the initial adoption proportion $q$ selected for the network.

(2)

With probability $P$, randomly select a pair of nodes and add an edge between them. There is at most one edge between any two distinct nodes, and no node can connect to itself.

4.2. Strategy Update Rule

In each game iteration, all participants play the game with each of their neighbors and accumulate their payoffs. This paper assumes that enterprises adopt the Fermi rule when updating their strategies. When enterprise $v_i$ updates its game strategy, it randomly selects a neighbouring enterprise $v_j$ for payoff comparison. The probability that enterprise $v_i$ will adopt the strategy of neighbour enterprise $v_j$ in the next game is:

$$\begin{array}{c}{P}_{\left(i\leftarrow j\right)}={\displaystyle \frac{1}{1+e^{\left(\frac{U_i-U_j}{k}\right)}}}\end{array}$$

(18)

where $U_i$ and $U_j$ represent the payoffs of enterprises $v_i$ and $v_j$, respectively, in the game, and $k$($k\ge 0$) represents the noise effect, measuring the intensity of the influence of external factors on individual behavior. As $k$ approaches infinity, individuals are more strongly influenced by external factors. Conversely, as $k$ approaches zero, individuals rely more on their own decisions.

5. Numerical Simulation Analysis

5.1. Parameter Initialization Setting

To investigate the influence of relevant coefficients on the diffusion of low-altitude UAV technology, the MATLAB R2024a software package was used to simulate and validate the evolutionary model dynamically. The experiment involves constructing an NW small-world network with $N = 100$ nodes, $K = 4$ neighbours per node, an initial proportion $q = 0.2$ of nodes adopting low-altitude UAV technology, a rewiring probability $P = 0.4$, a noise effect $k = 0.4$. As the core objective of the simulation is to accurately depict evolutionary laws through numerical settings, the initial values only impact the evolution’s amplitude and speed, not its overall trend [53]. Thereby, based on industry data from China’s low-altitude UAV logistics distribution field, relevant literature, and expert advice, this paper sets the initial parameters as follows:

According to statistics from the China State Post Bureau, China’s express delivery volume reached 174.5 billion items in 2024, with an expected increase to 190 billion items in 2025 [54]. For the purposes of calculation, the market demand is standardized as $Q=200$, and the potential increase in market share for an enterprise adopting low-altitude UAV technology is set as $\lambda =20$. The most intuitive manifestation of consumer perceived value is logistics efficiency. PwC’s assessment shows that drone delivery can reduce delivery time by approximately 10 min, and Meituan’s drone operation report also indicates an average delivery time of about 12 min, improving efficiency by around 150% compared to traditional delivery methods [55]. Accordingly, the consumer-perceived value benefit for traditional technology is set at $w=10$, and at $∆w=15$ for low-altitude UAV technology. Taking Meituan UAV delivery as an example, the average UAV delivery price for a 2 km delivery is 12 yuan, while the manual delivery price is 3 yuan. Therefore, $p^l=12 \mathrm{a}\mathrm{n}\mathrm{d} p^t=3$. Regarding logistics cost measurement, in addition to the one-time purchase cost of UAVs, operating costs covering maintenance, infrastructure, and labour must also be considered. However, existing literature provides limited specific analysis of UAV costs. Therefore, this paper only considers the unit delivery cost, setting the unit cost for UAVs and traditional delivery within a 2 km distance as 0.4 yuan and 0.6 yuan, respectively [56]. Additionally, the penalty for constraints on low-altitude UAV diffusion is set as $c=24$. The impact coefficient of government subsidies on the maturity of low-altitude UAV technology applications is set as $\beta =0.1$, and the initial maturity of low-altitude UAV technology applications for cluster core and Marginal Enterprises is set as ${\tau }_A=0.6 \mathrm{a}\mathrm{n}\mathrm{d} {\tau }_B=0.4$. The value for these parameters are as

Table 5. Initial Parameter Settings.

$\mathit{N}$	$\mathit{K}$	$\mathit{q}$	$\mathit{k}$	$\mathit{P}$	$\mathit{\lambda }$	$\mathit{Q}$	${\mathit{c}}_{\mathbf{t}}$	${\mathit{c}}_{\mathbf{l}}$	$\mathit{c}$	$\mathit{w}$	$\mathsf{∆}\mathit{w}$	${\mathit{p}}^{\mathit{l}}$	${\mathit{p}}^{\mathit{t}}$	${\mathit{\tau }}_{\mathit{A}}$	${\mathit{\tau }}_{\mathit{B}}$	$\mathit{\beta }$
100	4	0.2	0.4	0.4	20	200	0.6	0.4	24	10	15	12	3	0.6	0.4	0.1

.

5.2. Impact of Government Intervention on Low-Altitude UAV Technology Diffusion

Figure 2 shows the diffusion rate of low-altitude UAV technology among cluster Core Enterprises and Marginal Enterprises when the government implements no subsidy mechanism and does not intervene in the diffusion $(s=0,v=0, c=24)$, under values of $\lambda =0, 20, 40, 60, 80$. The simulation results indicate that, even with high consumer preference for low-altitude UAV technology, the technology fails to diffuse effectively among cluster enterprises without any government intervention. Ultimately, no enterprise adopts the technology. These results demonstrate that government intervention is necessary to promote the successful diffusion of low-altitude UAV technology among cluster enterprises.

5.3. Impact of Government Subsidies to Manufacturers on Low-Altitude UAV Technology Diffusion

To reveal the impact of government subsidies on the diffusion of low-altitude UAV technology among cluster core and Marginal Enterprises, a visual analysis was conducted with $v$ set to 12.25, 12.55, 12.85, 13.25, and 14.55. The results are shown in Figure 3. Figure 3a shows that increasing government subsidies to manufacturers significantly enhances the diffusion rate of low-altitude UAV technology among Core Enterprises. Furthermore, the speed of technology diffusion among Core Enterprises gradually accelerates as subsidy intensity increases. This is because increasing subsidies to manufacturers improves the development level of low-altitude UAV technology and promotes enterprises to achieve greater maturity in the application of low-altitude UAV technology, thereby reducing costs and increasing benefits for cluster enterprises. However, for Marginal Enterprises, the potential risk losses outweigh the expected benefits due to their lower maturity of low-altitude UAV technology applications. Therefore, diffusion only occurs under higher subsidy levels.

5.4. Impact of Government Subsidies to Enterprises on Low-Altitude UAV Technology Diffusion

To analyse the impact of government subsidies on the diffusion of low-altitude UAV technology among enterprises, the subsidy level was set to 18.55, 19.35, 19.55, 20.35, and 22.55. The simulation analysis examined how different subsidy levels influenced the diffusion evolution process and outcome among enterprises. Figure 4a shows the simulation results: When the government subsidy level is low, the diffusion rate of low-altitude UAV technology gradually decreases over time and approaches 0. As the subsidy level increases, the diffusion rate of low-altitude UAV technology among enterprises accelerates. A significant difference in response to government subsidies was observed between core and Marginal Enterprises within the cluster: under the same subsidy level, Core Enterprises showed greater enthusiasm for adopting low-altitude UAV technology, whereas Marginal Enterprises only initiated diffusion once the subsidy level had reached a certain threshold. This implies that Marginal Enterprises with lower technological maturity are less sensitive to government subsidies and exhibit lower enthusiasm for adopting the technology.

5.5. Impact of Constraint Penalty on Low-Altitude UAV Technology Diffusion

The constraint penalty $c$ was set to 24, 34, 44, 54, and 64 in the model parameter assignment to explore the effect of constraints on the diffusion of low-altitude UAV technology. As can be seen in Figure 5, the simulation results clearly reveal that constraints are a key factor affecting the diffusion rate of low-altitude UAV technology—the higher the constraint penalty, the slower the diffusion of technology. Once the constraint penalty reaches a certain threshold, the potential benefits of adopting low-altitude UAV technology for enterprises are outweighed by the losses caused by the penalty. At this point, enterprises are likely to reject the technology, which ultimately leads to the failure of low-altitude UAV technology diffusion.

6. Conclusions and Implications

6.1. Research Conclusions

This study established a complex network evolutionary game model to simulate the diffusion mechanism of low-altitude UAV technology under government policy guidance and real-world constraints. The research was designed to address several key objectives: to model the diffusion process, to empirically analyze the impact of government subsidies and development constraints, and to account for enterprise heterogeneity. Based on expert opinions and real-world data, we analyzed the impact of various factors on system diffusion. The main conclusions, which directly answer our research objectives, are as follows:

(1)

Addressing the core influencing factors: This study sought to identify the core factors influencing enterprises’ strategic choices. We conclude that these factors are threefold: (a) direct government subsidies to enterprises adopting the technology, which lower initial investment risks; (b) government subsidies to UAV manufacturers, which accelerate technological maturity and indirectly lower costs for adopters; and (c) the practical constraints on diffusion (e.g., airspace restrictions, safety risks, infrastructure shortcomings), which act as significant penalties and barriers to adoption.

(2)

Validating the efficacy and nuance of subsidy mechanisms: A primary objective was to empirically test the impact of government subsidies. We conclude that subsidy mechanisms are not merely beneficial but are essential for successful diffusion. Without them, diffusion fails. The simulation further reveals that diffusion rate increases with subsidy intensity and that the critical threshold for adoption is higher for Marginal Enterprises than for Core Enterprises, highlighting the need for differentiated policy.

(3)

Quantifying the impact of development constraints: This research aimed to integrate and quantify the tangible effects of real-world constraints. We conclude that constraints such as airspace issues and safety risks are pivotal negative factors. The diffusion rate decreases proportionally as the “penalty” from these constraints increases. When constraints are severe, they completely negate the positive effects of subsidies and lead to diffusion failure, underscoring the necessity of parallel regulatory and infrastructural policies.

6.2. Implications

(1)

This study makes significant contributions to social sustainable development at both theoretical and practical levels. Theoretically, it innovatively integrates complex network theory with evolutionary game theory to construct a dynamic model of low-altitude UAV technology diffusion, systematically revealing for the first time how government policies influence the diffusion process through networked interactions. The model captures the multiple sustainability benefits arising from the adoption of low-altitude UAV technology, including but not limited to reducing carbon emissions, enhancing agricultural productivity, and strengthening environmental monitoring capabilities. On the practical front, the research outcomes provide policymakers with a robust evidence-based foundation. Through comparative analysis within a unified framework, the study elucidates the relative effectiveness and sensitivity of different subsidy strategies (targeting manufacturers versus adopting enterprises), quantifies the impact of key constraints, and offers practical solutions for designing more effective policy instruments to accelerate the low-carbon transition driven by low-altitude UAV technology.

(2)

Based on the above conclusions, this paper proposes the following policy recommendations: Governments should establish targeted subsidy mechanisms, offering differentiated support—such as higher and longer subsidies for Marginal Enterprises—to overcome adoption barriers, while providing standardized incentives for Core Enterprises. Concurrently, subsidies should be directed to manufacturers to accelerate technological maturity and reduce costs. Furthermore, governments must actively mitigate constraints by accelerating the formulation of airspace and safety regulations, implementing integrated pilot programs in selected clusters to create demonstrable models for broader replication.

(3)

The findings offer clear guidance for key industry stakeholders: Enterprise managers should pursue first-mover advantages by aligning early adoption with government pilot programs and actively engaging in policy design. UAV manufacturers are advised to focus innovation on addressing core constraints—such as sense-and-avoid technology and noise reduction—to enhance product attractiveness. Meanwhile, industry consortia play a vital role in fostering collective action: disseminating best practices, establishing uniform standards, and promoting knowledge-sharing to reduce costs and risks, especially for marginal enterprises.

This paper makes theoretical and practical contributions to the field of research on socially sustainable development. From a theoretical perspective, it combines complex network structures with evolutionary game theory in order to model government subsidy mechanisms and constraints on the diffusion of technology, aspects which have been insufficiently explored in existing research on the diffusion of low-altitude UAVs. This integration reveals how government policy influences the diffusion of low-altitude UAV technology through network-mediated evolution, thereby promoting sustainable social development. In practice, the paper conducts a comprehensive comparative analysis of government subsidy mechanisms within a unified modelling framework. This demonstrates the effectiveness and sensitivity of subsidies for manufacturers versus cluster enterprises and provides insight into the significant impact of diffusion constraints.

However, this study has certain limitations. The diffusion of low-altitude UAV technology is a complex, top-down process that typically requires comprehensive consideration of manufacturers, suppliers, and consumers. This paper simplified these factors in order to focus more clearly on the impact of government policy. Secondly, the research assumes a uniform strategy update rule for all nodes, whereas, in reality, different nodes may have different update rules. Finally, as the low-altitude UAV industry is still in the early stage of development, accurate and publicly available data on large-scale commercial operations are relatively scarce, which results in certain limitations in the parameter setting of this paper. Future research can construct a two-layer network involving upstream and downstream supply chain enterprises, pay close attention to the development of this field, and conduct more in-depth empirical calibration and verification of model parameters as more operational data becomes publicly available. This will further enhance the accuracy of the research, improve the network environment update rules, and reveal more conclusions and implications.