Collaborative innovation in the UAV industrial chain: a two-layer network evolutionary game model

1 Introduction

In recent years, there has been a notable surge in the research, development, and deployment of Unmanned Aerial Vehicles (UAVs), which have emerged as a pivotal catalyst in the transformation and enhancement of associated sectors [1]. Nevertheless, the rapid progression of the UAV industry faces several obstacles, including persistent technological and public acceptance barriers, insufficient collaborative innovation between upstream and downstream enterprises, uneven distribution of innovation resources, and an incomplete market application ecosystem [2]. The Chinese government has issued a series of policy documents, including the Guidelines for the Construction of the Low-Altitude Economy Standard System (2026) and the revised Civil Aviation Law (2025), with the aim of comprehensively boosting the innovation efficiency and core competitiveness of the UAV industry [3] As a paradigm of a technology- and knowledge-intensive industry, the UAV sector derives its value-creation potential from continuous foundational technological breakthroughs and the successful assimilation of industrial application know-how [4]. Thus, fostering collaborative innovation and knowledge exchange between upstream UAV manufacturers and downstream service providers is essential for optimizing industrial resource allocation, expediting technological advancement, and broadening market opportunities.

The value of the low-altitude economy is reflected in the resolution of problems that arise in specific application scenarios [5]. Numerous practical experiences have proved that initiating from specific application scenarios and employing “reverse innovation” is a viable strategy for expediting technological iteration and enhancing industrial maturity [6]. This method aids upstream manufacturers in precisely identifying downstream application needs and guiding technology research and development efforts. Moreover, it allows downstream service providers to obtain cutting-edge technical support and solutions, thereby improving service quality and operational efficiency to better address varied and individualized market demands [7]. Recent collaborations across the UAV industrial chain illustrate this dynamic. In China, Meituan UAV and Xiling Zhihang have continuously adapted delivery mechanisms and auto-landing systems based on urban logistics data [8]. In Australia, XAG and Oztech have jointly optimized spraying algorithms and wind-resistant operational strategies for Australian broadacre farming [9]. In Germany, Quantum Systems and Skyports Drone Services have launched the ‘Overwatch’ surveillance-as-a-service offering, combining Quantum’s unmanned platforms with Skyports’ global operational and regulatory expertise [10]. As these UAV industry cases illustrate, collaborative innovation connecting upstream manufacturers and downstream service providers is critical to translating technical know-how into operational gains, which further facilitates technological upgrading and market expansion. Accordingly, establishing a sound collaborative innovation network that enables diverse stakeholders in the industrial chain to share technologies, patents, R&D experience, test data, market feedback, and other information facilitates the integration and reconfiguration of cross-linked technologies [11]. This approach transcends the geographical and organizational barriers typically associated with conventional innovation models and enables the rapid diffusion, aggregation, and upgrading of industrial innovations [12].

Nonetheless, akin to other sectors, the collaborative innovation choices between upstream and downstream entities in the UAV industrial chain are affected by several circumstances. This encompasses the technical accumulation levels of enterprises, the extent of trust in connections, capabilities for information absorption and transformation, as well as the costs and policy incentives associated with collaboration [13]. Moreover, as autonomous market entities aiming to safeguard their interests, manufacturers and service providers frequently demonstrate a protective inclination towards their fundamental technology assets. It has been shown that such enterprises typically engage in cooperative efforts only when the expected collaborative advantages are considered sufficient to outweigh their projected input costs and potential hazards [14]. This highlights the crucial role of government in promoting and encouraging industrial collaborative innovation. The establishment of scientifically valid policy intervention mechanisms, including research and development subsidies, application demonstrations, and tax incentives, has been shown to significantly affect enterprises’ willingness to participate in collaborative efforts and the strategic options accessible to them [15]. It can thus be concluded that collaborative innovation decisions between actors in the UAV industrial chain are essentially a dynamic strategic interaction process based on a trade-off between benefits and costs.

Within the UAV industrial ecosystem, upstream manufacturers and downstream service providers function as autonomous decision-making entities. In circumstances characterized by a lack of information and environmental uncertainty, the behavior exhibited by the subjects demonstrates clear characteristics of bounded rationality. This finding is in alignment with the fundamental assumptions of evolutionary game theory [16]. Simultaneously, within the genuine industrial ecosystem, several manufacturers and service providers create complex and interrelated “many-to-many” connection networks via industry platforms, trade groups, and geographic clusters. This phenomenon bestows inter-enterprise collaborative innovation behavior with characteristic complex network attributes [17]. While classic evolutionary game theory can elucidate macro-evolutionary patterns of group strategic interactions, it often fails to accurately represent micro-level interactions and the diffusion of strategies among individual players within localized network structures [18]. Consequently, the research methodology combining complex network theory with evolutionary game theory has been widely applied in fields such as industrial collaboration and innovation networks. This paper, using the lens of complex network evolutionary game theory, seeks to thoroughly investigate the following fundamental questions:

• In what manner do collaborative innovation behaviors develop between UAV manufacturers and service providers within the constraints of bounded rationality and networked interactions?
• In what manner do essential elements—collaboration expenses, policy incentives, technological accumulation, knowledge absorption and transformation capabilities, and faith in cooperation—impact the equilibrium and convergence velocity of the collaborative innovation system?
• In what ways may policy formulation and mechanism enhancement facilitate the transition of the UAV industrial chain from basic coordination to advanced cooperation efficiency?

This paper is structured as follows: Section 2 of this work presents a literature survey, whereas Section 3 develops an evolutionary game model to examine collaborative innovation between upstream and downstream enterprises and conducts a stability analysis. Section 4 presents a complex network architecture aimed at developing a collaborative innovation network evolutionary game model. Section 5 conducts numerical simulations and analyzes the results. Ultimately, Section 6 summarizes the research conclusions, compares existing studies, and puts forward policy recommendations.

2 Literature review

2.1 Research on the UAV industry

UAVs serve as a vital foundation for the advancement of the low-altitude economy, integrating technology from several domains including aerial photography, intelligent sensing, and communication navigation. They are spearheading the development of a new digitalized, interconnected, and intelligent airspace application ecosystem [19–21]. UAVs are revolutionizing traditional aviation operational frameworks and providing crucial technological support for the modernization of diverse sectors, including logistics, inspection, agriculture, and emergency response, while also profoundly influencing future social sustainability development [22]. Consequently, prominent nations worldwide have identified the UAV industry as a vital development sector, actively promoting its industrialization through initiatives that include advancing technological research and development, conducting application demonstrations, improving regulations and standards, and enacting supportive policies.

Simultaneously, academic research related to the UAV market has expanded considerably. Contemporary study on the industrial development environment primarily focuses on airspace management policy formulation, the establishment of regulatory and standardization frameworks, and infrastructure planning [23, 24]. Scholars highlight critical areas in technological research and development, including flight control systems, autonomous navigation and obstacle avoidance technologies, onboard sensor integration, endurance enhancement, and data link security [25–27]. Research in industry management and supervision frequently focuses on operational safety risk assessment, airworthiness certification systems, privacy protection, and airspace traffic management technologies [28, 29]. The current literature mostly examines UAV industry development through the lenses of macro-policies, technological advancement, and regulatory frameworks, emphasizing research on technology roadmaps and policy structures. However, there is a lack of thorough research about the micro-decision-making mechanisms, dynamic evolutionary processes, and diffusion patterns inside the networked structures of collaborative innovation among upstream and downstream partners in the industrial chain.

2.2 Complex network evolutionary game

Complex network evolutionary game theory is a significant analytical framework resulting from the merger of evolutionary game theory with complex network research. It analyzes the dynamic process of group interactions derived from conventional evolutionary games inside non-homogeneous, organized network linkages [30]. Unlike the “uniform mixing” population typically assumed in conventional evolutionary games, this method emphasizes that real individuals are usually embedded within specific social or industrial networks. Their strategy alteration relies not solely on payoff assessments but is also influenced by their local network peers, enabling a more precise depiction of the micro-mechanisms that govern strategy diffusion, cooperative emergence, and the evolution of network structure [31, 52]. The analysis of industrial collaboration and innovation ecosystems reveals that the decision-making behaviors of enterprises or institutions often generate complex networks of connections through processes such as supply chains, R&D partnerships, and geographical closeness. Their strategic development exhibits distinct spatial dependence and structural embeddedness, making complex network evolutionary game theory an invaluable theoretical framework for clarifying the relationship between macro-dynamics and micro-interactions inside a system [32].

This strategy is presently utilized extensively in research across various domains, including innovation networks, supply chain collaboration, and technology diffusion. Zhang et al. developed a complex network game model to examine the adoption behavior of blockchain technology in logistics service supply chains [33]. Fu et al. developed a complex network evolutionary game model to examine the impact of regulatory incentives on the proliferation of battery-swapping practices among new energy taxis [34]. Chen et al. established a novel analytical framework that elucidates the impact of various network architectures and diffusion processes on the propagation of low-carbon policies [35]. Tao employed cooperative patent data and combined social network analysis with a complex network evolutionary game model to develop collaborative invention networks, thereby examining the determinants affecting the evolution of patent cooperation [36]. Wu et al. developed an evolutionary game model to examine the dissemination process of green packaging within logistics clusters in a complex network framework [37].

In summary, although current research on the UAV industry has produced significant findings, it primarily concentrates on UAV industry policies, technologies, and regulations. There is an insufficient exploration of the dynamic evolutionary mechanisms of multi-agent collaborative innovation within the industrial chain and its diffusion patterns in networked systems. Limited research systematically outlines the strategy adjustment process of UAV upstream and downstream enterprises under conditions of bounded rationality and localized interaction, nor does it sufficiently clarify how network topology affects the propagation and stabilization of collaborative innovation behavior. This study emphasizes the importance of integrating complex network evolutionary game theory to align with the real interaction framework of the UAV industry and to analyze the dynamic evolutionary mechanisms of strategic synergy between UAV manufacturers and service providers. This method may characterize the micro-level decision-making and learning mechanisms of enterprises inside specific network connections and expose the macro-level impact of multi-factor coupling on the system’s evolutionary equilibrium. Thus, it offers a more sophisticated and dynamic theoretical framework for comprehending and directing collaborative innovation within this sector [38].

This paper’s research contributions are primarily evident in three areas [1]: It develops an evolutionary game model for the nascent UAV industrial chain, incorporating collaborative innovation costs, policy incentives, and multi-dimensional enterprise capabilities, thereby elucidating the dynamics of collaborative innovation evolution [2]. It incorporates a complex network architecture into the evolutionary game analysis, creating a two-layer network game model with a “preferential attachment” characteristic, delineating the interactive impact between local interactions and global dissemination [3]. Through numerical simulation, it systematically delineates the sensitivity of system evolution across various parameter scenarios and the threshold effects of policy intervention, offering references of both theoretical and practical significance for the government and enterprises to foster collaborative innovation within the UAV industrial chain.

3 Game model of UAV industrial chain collaborative innovation

The collaborative innovation process within the UAV industry chain primarily engages two key parties: upstream manufacturers and downstream service providers. Manufacturers, as advanced entities at the upstream segment of the industrial chain, generally possess essential technological competencies like UAV overall design, core component research and development, and production methodologies. Their goods offer solutions for various sectors. Downstream service providers function at the application level, concentrating on delivering UAV operations, application integration, and post-sales services for particular sectors such as logistics, inspection, and agricultural pest management. They have amassed extensive scenario-specific application knowledge and client demand data. Consequently, creating a collaborative innovation system can connect the technological supply from manufacturing with the market application requirements from the service sector, thereby facilitating technological advancement and enhancing the industrial ecosystem. The diagram of UAV industrial chain collaborative innovation network is shown in Figure 1.

3.1 Basic model assumptions

This study examines the divergent collaborative innovation methods of upstream and downstream enterprises within the UAV industrial chain, utilizing pertinent research findings and the current context of the UAV industry. Elements including fundamental profit, cost of collaborative innovation, cost sharing, government subsidies, technological maturity, and risk loss are incorporated into the profit functions of manufacturers and service providers to develop an evolutionary game model. This seeks to elucidate the dynamic processes and stability conditions of their strategic interactions, thereby establishing a foundation for pertinent policy formulation. The fundamental premises of the model are as follows:

Assumption 1 The number of manufacturers engaged in manufacturing UAVs is M . Based on a comprehensive consideration of their own interests, enterprises can choose whether to participate in collaborative innovation. It is proposed that x denote the proportion of manufacturers who elect to participate. The number of service providers adopting UAV technology is represented by N , with y being the proportion choosing to participate in collaborative innovation. It is an accepted academic premise that organizations arrive at decisions by means of the principle of bounded rationality. The strategy set is defined as {Participate in Collaborative Innovation, Not Participate in Collaborative Innovation}, with the objective of maximizing market competitiveness x , y ∈ 0 , 1.

Assumption 2 Let c i (i = m , s denote the cost for manufacturers to produce UAVs and for service providers to offer UAV services. For manufacturers, c m includes R&D expenditures for core components, composite material costs, and production assembly expenses. For service providers, c s includes operational costs, personnel training, equipment maintenance, and airspace application fees. In the provision of UAV services, providers face a technology adoption risk loss μ due to imperfect low-altitude infrastructure and inadequate regulatory frameworks. Following the cost structure established in our previous work, the service cost and risk loss are non-linearly related to UAV technology maturity τ , expressed as c s + μ e − τ [39].

Assumption 3 Drawing on the policy framework of China’s low-altitude economy development, government subsidy policies are formulated based on dual objectives. First, to provide production cost subsidies to manufacturers at a rate s of the production cost, incentivizing technological R&D by manufacturers and promoting the technological maturity of UAVs. Second, to subsidize service providers’ service costs through means like consumption vouchers or purchase tax reductions, at a rate v of the cost of providing UAV services, aiming to increase the market share of UAV products.

Assumption 4 During the diffusion of UAV technology, if both manufacturers and service providers participate in collaborative innovation, each can obtain collaborative benefits. This benefit is closely related to the enterprise’s technological accumulation level k i , cooperation trust degree t i , and knowledge absorption and transformation capability a i . For manufacturers, k m reflects their proficiency in UAV overall design, core component R&D, and production processes; for service providers, k s reflects their expertise in scenario-specific applications. The cooperation trust degree t i reflects the willingness to share proprietary technical data and operational information. The knowledge absorption and transformation capability a i captures the ability to acquire and internalize externally sourced UAV-related technologies. Drawing on the modeling approach of Chen et al, the collaborative benefit can be expressed as w i = w i 0 k i t i a i i = m , s , where w i 0 is the benchmark benefit parameter [40].

Assumption 5 Collaborative innovation requires both parties to jointly bear the collaborative innovation cost c . The manufacturer bears a proportion λ , and the service provider bears a proportion 1 − λ . If only one party chooses to participate, that party must bear the full collaborative innovation cost c , cannot obtain collaborative benefits, but can receive government incentives such as tax rebates and policy support, denoted as f . If both parties actively participate in cooperation, they both enjoy the policy incentive f.

Assumption 6 The sales revenue for service providers from offering UAV services is U s , and the sales revenue for manufacturers from selling UAVs is U m. Both are higher than the collaborative innovation cost c . The profits for UAV manufacturers and service providers under the strategies of participating and not participating in collaborative innovation are denoted as π i C and π i D i = m , s , respectively.

The definitions of the model parameters are shown in Table 1:

TABLE 1. Model symbols and definitions.

3.2 Game payoff matrix

The game payoff matrix for UAV manufacturers and service providers under different strategy choices is shown in Table 2.

TABLE 2. Payoff matrix for UAV manufacturers and service providers.

Where:

π m C C = U m − 1 − s c m + w m − λ c + f (1)

π s C C = U s − c s + μ e − τ + v c s + w s − 1 − λ c + f (2)

π m C D = U m − 1 − s c m − c + f (3)

π s C D = U s − c s + μ e − τ + v c s (4)

π m D C = U m − 1 − s c m (5)

π s D C = U s − c s + μ e − τ + v c s − c + f (6)

π m D D = U m − 1 − s c m (7)

π s D D = U s − c s + μ e − τ + v c s (8)

The expected payoff for a UAV manufacturer choosing to participate in collaborative innovation is:

E m C = U m − 1 − s c m + y w m + c 1 − λ − c + f (9)

The expected payoff for a UAV manufacturer choosing not to participate in collaborative innovation is:

E m D = U m − 1 − s c m (10)

The average expected payoff for a UAV manufacturer over the choices of participating and not participating is:

E ¯ m = U m − 1 − s c m + x y w m + c 1 − λ − x c + x f (11)

The expected payoff for a service provider choosing to participate in collaborative innovation is:

E s C = U s − c s + μ e − τ + v c s + x w s + c λ − c + f (12)

The expected payoff for a service provider choosing not to participate in collaborative innovation is:

E s D = U s − c s + μ e − τ + v c s (13)

The average expected payoff for a service provider over the choices of participating and not participating is:

E ¯ s = U s − c s + μ e − τ + v c s + x y w s + c λ − y c + y f (14)

Based on the above payoff matrix, the replicator dynamic equations for UAV manufacturers and service providers are obtained:

F x = d x d t = x 1 − x y π m C C − π m D C + 1 − y π m C D − π m D D (15)

F y = d y d t = y 1 − y x π s C C − π s C D + 1 − x π s D C − π s D D (16)

3.3 Analysis of evolutionary stability

The decision-making dynamic evolution system is constructed on the basis of the replicator dynamic equations of UAV manufacturers and service providers. The equilibrium point configuration is determined by the conditions F x = 0 and F y = 0, which yield a total of five equilibrium points. The following equations are to be used: E 1 0 , 0 , E 2 0 , 1 , E 3 1 , 0 , E 4 1 , 1, and E 5 x * , y *, where x * = c − f w s + c λ , y * = c − f w m + c 1 − λ.

The stability of the local equilibrium points of the game system can be analyzed using the Jacobian matrix. In the event of an equilibrium point satisfying det ⁡ > 0 and t r < 0, it can be identified as an Evolutionarily Stable Strategy (ESS). The Jacobian matrix of the replicator dynamic equations is as follows:

J = ∂ F x ∂ x ∂ F x ∂ y ∂ F y ∂ x ∂ F y ∂ y = J 11 J 12 J 21 J 22 (17)

Where J 11 = 1 − 2 x y w m + c − c λ − c + f , J 12 = x 1 − x w m + c − c λ , J 21 = y 1 − y w s + c λ , J 22 = 1 − 2 y x w s + c λ − c + f

According to the method of stability analysis of the Jacobian matrix, the values of the determinant and the trace are calculated, as demonstrated in Table 3.

TABLE 3. The values of the determinant and the trace.

In accordance with the stability criterion, the trace of the internal equilibrium point E 5 x * , y * is tr ⁡ J = 0. This indicates that the aforementioned point does not constitute an ESS of the system. Moreover, it is imperative to note that, in order to satisfy the fundamental constraint of 0 < x * , y * < 1, the existence of x * and y * is contingent upon the premise of probability values. The substitution of x * = c − f w s + c λ reveals that x * and y * are positive only when c > f. This constraint c > f is evidently of practical significance, indicating that the policy incentive f should be designed as a partial compensation for the cost c, rather than full coverage. This approach precludes the occurrence of “pseudo-cooperation” among enterprises due to over-reliance on incentives, ensuring that collaborative innovation involves substantive resource investment and is market-oriented. It can thus be concluded that the ESS of the system under four different scenarios can be derived by classifying the logical relationships among model parameters. The evolutionary game equilibrium point analysis is shown in Table 4.

TABLE 4. Evolutionary game equilibrium point analysis.

Scenario 1. When w m + f > c λ and w s + f > c 1 − λ , the net benefits for both UAV manufacturers and service providers from participating in collaborative innovation exceed their respective cost shares. In this scenario, the system comprises two ESS: E 1 0 , 0 and E 4 1 , 1 . In the event of an auspicious initial collaborative atmosphere and a high level of mutual trust, the system will evolve towards full collaboration 1 , 1 . Conversely, should initial willingness to participate be found wanting, the system will fall into a locked state of “neither participating”.

Scenario 2. The condition w m + f > c λ is met, alongside the condition w s + f < c 1 − λ . This indicates that the total benefit for the UAV manufacturer from participation is greater than its cost share, while the total benefit for the service provider is less than its cost share. In this scenario, the ESS of the system is 0 , 0 . This finding suggests that, despite the motivation of manufacturers to engage in collaborative innovation, the absence of adequate incentives for service providers hinders the successful implementation of such endeavours.

Scenario 3. It is evident that when w m + f < c λ and w s + f > c 1 − λ, the service provider derives benefits from participation. However, the net benefit for the UAV manufacturer is negative. In contrast to the scenario 2, service providers are willing, but manufacturers lack the motivation to participate because the benefits of collaboration cannot cover their R&D and collaboration costs. The system is also found to be stabilized at E 1 0 , 0 , and the absence of technological supply has been identified as a key factor preventing collaboration.

Scenario 4. The condition w m + f < c λ is met, in addition to the condition w s + f < c 1 − λ . This indicates that the total benefits accruing to both UAV manufacturers and service providers from participating in collaborative innovation are less than their respective cost shares. In such circumstances, the unilateral participation of one party would invariably compromise their own interests, irrespective of the strategic actions of the other party. Consequently, the “not participating” strategy becomes the dominant approach for both parties, and the system undergoes a natural convergence towards E 1 0 , 0 , thereby illustrating a state of market failure.

In summary, parameters including collaborative innovation cost, policy incentive, technological accumulation level, knowledge absorption and transformation capability, and cooperation trust degree collectively determine the evolutionary direction of the collaborative innovation system in the UAV industrial chain. However, while the traditional evolutionary game model can identify the eventual evolutionary stable states of the five equilibrium points under four scenarios, it fails to capture the dynamic strategy adjustment processes of individual participants or to reflect the heterogeneity among agents in the population. In the UAV industrial chain collaborative innovation network, a large number of manufacturers and service providers form dense and intertwined “many-to-many” connections, endowing inter-enterprise collaborative innovation behavior with typical complex network characteristics. Relying solely on traditional evolutionary game theory makes it difficult to effectively capture the complex game interactions between the two parties within a networked structure. Therefore, the following sections of this paper will further investigate the evolutionary patterns of collaborative innovation strategies in the UAV industrial chain under the complex network environment.

4 Construction of the complex network model

4.1 Network construction

Within the context of the UAV industrial chain collaborative innovation system, as the number of manufacturers and service providers increases, the inter-enterprise relationships become increasingly complex, gradually evolving into a complex network with a two-layer structure. In this network, the decisions of enterprises are influenced by a combination of factors. Firstly, enterprises are affected by the payoffs from cross-group games. Secondly, enterprises are also influenced by social learning within their respective groups [41]. Specifically, the UAV manufacturer group and the service provider group each form an internal network. These are then interconnected through cross-group links to constitute a two-layer interactive system. Enterprises have been shown to drive the dynamic evolution of the overall cooperative state by pursuing payoff maximization in cross-group games and adjusting their own behaviors through strategy learning within their groups [42]. The present paper thus proposes a theoretical framework in the form of an evolutionary game model based on a two-layer complex network. The purpose of this model is to provide a more in-depth investigation into the evolutionary mechanisms of collaborative innovation behavior within the UAV industrial chain.

Extensive research indicates that socio-economic networks, including industrial chains and innovation networks, commonly exhibit scale-free properties, meaning a few nodes possess a large number of connections [43, 44]. The present paper employs a scale-free network (Barabási-Albert model) to simulate the respective subnetworks of UAV manufacturers and service providers. The manufacturer group is regarded as the upper-layer network, wherein each node represents a manufacturer, and the ranking of a node’s degree is indicative of its strength ranking based on technology, capital, and scale. The service provider group constitutes the lower-layer network, wherein each node represents a service provider, and its degree ranking corresponds to its strength ranking based on market share, technology application capability, and customer resources. The collaborative relationships between the two types of enterprises are represented by cross-layer connections between the two-layer networks.

UAV manufacturers and service providers clearly demonstrate a certain tendency for “preferential attachment” when choosing collaborative innovation partners. This tendency entails forming associations with organizations that exhibit greater overall strength in the alternative group. This strategic method facilitates access to enhanced resources and the achievement of increased collaborative innovation advantages. The precise construction algorithm is delineated as follows:

The initial step in the process is the generation of basic subnetworks. The subsequent generation of scale-free subnetworks, comprising M = 50 manufacturer nodes and N = 150 service provider nodes, respectively, was undertaken, along with the calculation of the degree of each node.

Secondly, the process of sorting nodes according to their degree. The nodes of the manufacturers and service providers must be sorted in descending order according to their degree values. This process will result in the creation of two new sequences: one that represents the degree ranking of manufacturers, and one that represents the degree ranking of service providers.

Thirdly, the selection of a number of top-ranked core nodes from both sequences is imperative for the establishment of full connections among them.

Fourthly, the utilization of preferential attachment for the purpose of facilitating extended connections is to be recommended. In the context of a manufacturer node that has been assigned a rank of i (where i denotes the total number of core nodes), it is recommended that service provider nodes be selected with a preference for those that are already connected to the manufacturer network. This selection is based on their degree-weighted probability, with the objective of establishing new connections. In a similar manner, for a service provider node that has been ranked at position j (where j > number of core nodes), it is recommended that q manufacturer nodes are selected from its current connection pool in order to establish links.

Finally, all cross-layer connection relationships are recorded in a matrix, thereby forming a UAV industrial chain two-layer network that maps reality and features preferential attachment, as demonstrated in Figure 2.

4.2 Algorithm settings for network game

The integration of the realities of the UAV industry with the general framework of complex network games gives rise to the following fundamental assumptions [35, 42]:

Assumption 1. It is hypothesized that UAV manufacturers and service providers are boundedly rational agents. The selection of a strategy is related to the magnitude of expected payoffs; however, optimal decisions are not invariably made, and there is a certain probability of an alternative strategy being chosen.

Assumption 2. In the context of updating strategies, it is postulated that each enterprise will engage in a comparison of its payoff with that of its immediate neighbors within the confines of its own subnetwork.

Assumption 3. It is hypothesized that UAV manufacturers and service providers adhere to a uniform strategy for learning and updating rules. The strategy update is predicated on a comparison of payoffs from the preceding round of games with those of their neighbors.

Assumption 4. The present study operates under the assumption that an enterprise’s collaborative innovation payoff originates solely from its directly connected cross-layer neighbors. It is evident that enterprises are not in direct competition with external entities outside the network.

Furthermore, enterprises within the network update their strategies for the subsequent round through imitation based on the Fermi rule [45]. The UAV manufacturer network can be denoted as W m i , l i m , s i m, where i = 1 , 2 , . . . , M represents the manufacturer members, l i m is its node degree, and s i m is its game strategy. The service provider network is denoted by the following equation: W s j , l j s , s j s, where j = 1 , 2 , . . . , N and l j s represents the node degree of the service provider, while s j s denotes its game strategy. The evolutionary algorithm for the network game is as follows:

Step 1: The initial step in the process is the calculation of the game payoff. In each evolutionary round, each enterprise calculates its total payoff from playing games with all its cross-layer neighbors.

The total payoff for UAV manufacturer i is defined as the sum of its payoffs from games with all connected service providers j ∈ Ω i s.

P i m = ∑ j ∈ Ω i s s i m A i j s j s T

In this study, Ω i s denotes the set of all neighbors of manufacturer i in the lower-layer service provider network. The strategy vectors s i m and s j s are also defined, and A i j is the game payoff matrix shown in Table 2. Analogously, the total payoff for service provider j is:where Ω j m is the set of all neighbors of service provider j in the upper-layer manufacturer network.

P j s = ∑ i ∈ Ω j m s i m A i j s j s T

Step 2: The second step in the process is to undertake an update of the strategy and to consider the issue of imitation. Subsequent to each game round, the enterprises recalibrate their strategies within their respective subnetworks in accordance with the Fermi rule. The UAV manufacturer will randomly select a neighboring manufacturer h from its manufacturer network W m (i.e., h ∈ N i m, where N i m denotes the set of manufacturers that are located in the same network as manufacturer i). This selection will be made for the purpose of payoff comparison. In the subsequent round, there is a probability of W i → h that the strategy employed will be the same as that of the neighbor.

W i → h = 1 1 + exp ⁡ η P i m − P h m

In a similar manner, service provider j randomly selects a neighbouring service provider l within its service provider network W s (i.e., l ∈ N j s, where N j s denotes the set of neighbours of service provider j in the service provider network) for the purpose of payoff comparison. In the subsequent round, the probability of adoption of the neighbor’s strategy is W j → l.

W j → l = 1 1 + exp ⁡ η P j s − P l s

In this context, the parameter η > 0 is indicative of the intensity of noise in the environment or the strength of rationality.

Step 3: The first two steps are then repeated for multiple rounds of evolutionary iteration. Following the conclusion of each iteration, the degree of cooperation within both the manufacturer group and the service provider group is documented.

Step 4: Following a sufficient number of iterations, the strategy distribution of the system tends to stabilize. The final step involves the calculation of the stabilized average cooperation level, which is then utilized as the foundation for the ensuing analysis. The framework of the network construction and strategy update algorithm is illustrated in Figure 3.

5 Numerical simulation and analysis

5.1 Parameter setting

As a pioneering country in the development of the low-altitude economy, China has fostered a full-spectrum UAV industrial chain integrating R&D, manufacturing, testing, and application, in which collaborative innovation serves as the core engine for technological breakthroughs and industrial upgrading. To clearly compare the marginal effects of core parameters and their sensitivity across diverse parameter settings, numerical simulations are conducted, with reference to China’s UAV industry data, to verify the rationality and effectiveness of the proposed model.

Baseline parameters are determined by combining China’s industrial support policies for UAVs, standard parameter value conventions in existing literature, and the realistic operating scale of medium-sized civil UAV enterprises across China. The parameter settings are specified as follows: manufacturer’s sales revenue U m = 15, production cost coefficient c m = 8; service provider’s service revenue U s = 12, operation cost coefficient c s = 5 (unit: million RMB). Two government subsidy coefficients s = 0.1 and v = 0.5 are set to explore how differentiated subsidy schemes affect the evolution of collaborative innovation. The technology adoption risk loss borne by service providers is assigned as μ = 2, representing the potential risk level caused by inadequate infrastructure and uncertain operating environments. UAV technological maturity is defined as τ = 0.65, indicating that logistics UAVs are currently at a medium-high maturity stage. The initial proportion of cooperating players x = 0.3 and y = 0.3, and the environmental noise parameter η = 0.1. The complete game parameter configurations under all scenarios are listed in Table 5.

TABLE 5. Game parameter settings in various scenarios.

5.2 Validation of model validity

Figure 4 illustrates the evolutionary paths of the collaborative innovation system under four different scenarios, from the initial state to the stable equilibrium. In Scenario 1, the theoretical local stability analysis of the evolutionary game model suggests two possible outcomes: 0 , 0 and 1 , 1. For the simulation experiment presented in this paper, the system under Scenario 1 converges to 1 , 1, indicating that the cooperation proportions of both UAV manufacturers and service providers evolve towards full collaboration. In Scenarios 2 to 4, the cooperation proportions of both parties converge to 0, which is consistent with the theoretical ESS of 0 , 0 derived from the evolutionary game model.

The conclusions drawn from the two-layer network evolutionary game model are consistent with the local stability analysis results of the traditional evolutionary game model presented in Table 4. This consistency validates the effectiveness of the complex network evolutionary game model and confirms the rationality of the parameter settings. Furthermore, the equilibrium of the network game model in Scenario 1 exhibits two possible ESS outcomes: 0 , 0 or 1 , 1, depending on the system’s initial conditions. Given the bistable nature of the system, simulation experiments are conducted under Scenario 1 using the control variable method to systematically investigate how collaborative innovation cost, policy incentive, technological accumulation level, knowledge absorption and transformation capability, and cooperation trust degree affect the evolutionary dynamics of collaborative innovation decisions made by UAV manufacturers and service providers. To mitigate the influence of stochastic fluctuations, the final outputs are averaged over 20 independent simulation runs, and the corresponding results are shown in Figures 5–9.

5.3 Impact of collaborative innovation cost on network evolution

In the context of a collaborative innovation process between UAV manufacturers and service providers, disparities in revenue and cost structures between the parties are likely to result in divergent costs of collaboration. It is demonstrated in Figure 5 that, under the condition that other parameters remain constant, the impact of the cost of collaborative innovation on network evolutionary dynamics is illustrated. The simulation results indicate that when the collaborative innovation cost is high, both manufacturers and service providers tend to refuse participation. Conversely, as this cost decreases, there is a clear upward trend in the proportion of cooperation from both parties. Further observation reveals a heightened sensitivity among manufacturers with regard to alterations in the costs of collaborative innovation in comparison to service providers. In the event of a cost increase, manufacturers transition from a state of cooperation to a state of non-cooperation at a rate that is significantly faster than that of service providers.

5.4 Impact of policy incentives on network evolution

The present study investigates the impact of policy incentives on network evolutionary dynamics. To this end, the level of collaborative innovation policy incentive provided by the government is set as f ∈ 2.0 , 2.5 , 3.0 , 3.5 , 4.0. The simulation results are displayed in Figure 6. The findings indicate that augmenting policy incentives can substantially augment the propensity of UAV manufacturers and service providers to engage in collaborative innovation, thereby fostering a rapid escalation in the cooperation proportion towards a stable level. However, when government policy incentives are insufficient, the evolutionary speed at which firms switch from non-cooperative to cooperative strategies gradually declines, and the cooperation level trends toward a low value.This phenomenon suggests that in instances where policy incentives are inadequate to cover potential risk losses and collaborative innovation costs, the participation benefits for enterprises cannot be assured. Consequently, enterprises may lack the intrinsic motivation to engage in collaborative innovation.

5.5 Impact of technological accumulation level on network evolution

As demonstrated in Figure 7a, an escalation in the technological accumulation level k m of UAV manufacturers is associated with a gradual acceleration in the evolutionary rate of manufacturers’ participation in collaborative innovation, which in turn results in an increase in the final cooperative equilibrium level. Furthermore, Figure 7b demonstrates that an enhancement in the service providers’ technological accumulation level, denoted by k s, concomitantly expedites their evolutionary process of participation and fosters a more pronounced cooperative steady state. This finding suggests that, for both manufacturers and service providers, enhancing their technological accumulation level can substantially boost the motivation and efficiency of their respective groups in participating in collaborative innovation. The technological accumulation level has been demonstrated to boost the collaborative innovation benefit w i, thereby prompting the system to converge at an accelerated rate towards a high-cooperation-rate equilibrium. Consequently, within the collaborative innovation network, the development of enterprises’ technological capabilities can propel the collaborative evolution of the entire industrial chain.

5.6 Impact of knowledge absorption and transformation capability on network evolution

The present study sets out to analyze the impact of the enterprises’ knowledge absorption and transformation capability, which is represented by the parameter a i = 0.2 , 0.4 , 0.6 , 0.8 , 1.0, on the participation of UAV manufacturers and service providers in collaborative innovation. As demonstrated in Figure 8, in circumstances where the knowledge absorption and transformation capability is limited, the enthusiasm of UAV manufacturers and service providers to participate is also limited, resulting in a sluggish progression of the system towards a cooperative equilibrium. As this capability improves, the diffusion rate of collaborative innovation behavior within the network increases significantly. This finding suggests that enterprises’ capacity for knowledge absorption and transformation is a pivotal factor in the evolutionary dynamics of collaborative innovation. A higher capability signifies that enterprises are able to more efficiently transform external knowledge into their own innovation capacity. This, in turn, results in an augmentation of the collaborative innovation benefit w i, an enhancement of the net benefit from participation, and an acceleration of the system’s convergence towards a high-cooperation-rate equilibrium.

5.7 Impact of cooperation trust degree on network evolution

The cooperation trust degree of UAV manufacturers t m ∈ 0.2 , 0.4 , 0.6 , 0.8 , 1.0 and that of service providers t s ∈ 0.3 , 0.7 , 1.1 , 1.5 , 1.9 are set separately to examine the impacts of cooperation trust degree on network evolutionary dynamics, and the simulation results are shown in Figure 9. There is a substantial positive correlation between cooperation trust and the diffusion rate of collaborative innovation behavior within the network. As the degree of cooperation among enterprises increases, there is a concomitant enhancement in their enthusiasm to participate in collaborative innovation, and the system evolves more rapidly towards a cooperative equilibrium. This finding suggests that cooperation trust is a significant non-technical factor influencing the evolution of the industrial chain’s collaborative innovation network. A higher degree of cooperation trust has been shown to be an effective means of improving the efficiency of transforming technological accumulation into collaborative innovation benefits. Furthermore, it has been demonstrated that such cooperation can reduce risks, promote knowledge sharing and resource integration, strengthen the willingness to cooperate among enterprises, and enable the system to converge faster towards a high-cooperation-rate equilibrium.

6 Conclusions and recommendations

6.1 Main conclusions

The present study is concerned with the issue of collaborative innovation between upstream manufacturers and downstream service providers in the UAV industrial chain. The construction of a two-layer network game model is initiated through the integration of evolutionary game and complex network theory. This model is then subjected to a systematic analysis, which aims to elucidate the impact of pivotal factors on the evolutionary dynamics of collaborative innovation behavior. The aforementioned factors encompass collaborative innovation costs, policy incentives, technological accumulation levels, knowledge absorption and transformation capabilities, and cooperation trust. This analysis is conducted through the utilization of numerical simulation techniques. The main conclusions are as follows:This study focuses on collaborative innovation behavior within the UAV industrial chain, illuminating its dynamic evolutionary pattern characterized by multiple equilibria and path dependence. In the context of bounded rationality and networked interaction, the collaborative system of manufacturers and service providers may converge to two stable states. The final equilibrium is found to be contingent upon the system’s initial state. This finding indicates that industrial collaboration does not develop in a straightforward, linear fashion. Instead, it is possible for this collaboration to become “locked” into a low-level equilibrium as a result of its historical path. This highlights the importance of external intervention and early cultivation.

Secondly, collaborative innovation cost and policy incentive represent pivotal exogenous factors influencing the evolutionary trajectory and velocity of collaborative innovation within the UAV industrial chain. The findings of the simulation suggest that a reduction in the costs of collaborative innovation has the potential to significantly enhance the willingness of manufacturers and service providers to participate. Concurrently, the policy incentive f furnished by the government exerts a direct influence on the convergence rate of enterprises’ cooperative evolution. In circumstances where the incentive level is inadequate to encompass the costs and risks inherent in collaborative innovation, the system is rendered susceptible to the maintenance of a low-level equilibrium characterized by “no participation”. This underscores the need for appropriate policy interventions.

Thirdly, internal capacity building is the intrinsic driver for the sustainable development of collaborative innovation. Increases in the technological accumulation level of manufacturers and of service providers have been shown to accelerate the speed of cooperation diffusion. Furthermore, the knowledge absorption and transformation capability of enterprises and their cooperation trust are crucial soft factors affecting the evolutionary efficiency of the collaborative innovation network. The ability to absorb higher levels of knowledge has been demonstrated to facilitate more effective translation of external collaborative outcomes into innovation capacity within enterprises. Furthermore, an increase in cooperation trust has been shown to significantly accelerate the propagation of collaborative behavior within the network.

6.2 Comparison with existing studies

Our findings engage with the existing literature across three dimensions: methodological contribution, thematic extension, and theoretical alignment.

First, regarding methodological reference. The complex network evolutionary game approach employed in this study builds upon a growing body of research applying this methodology to industrial collaboration problems. Zhang et al. [33] developed a similar framework to examine blockchain adoption in logistics supply chains, while Fu et al. [34] studied diffusion of battery-swapping taxis under regulatory incentives, and Chen et al. [35] analyzed low-carbon policy propagation among cities. Our results corroborate their common finding that policy incentives and cost reduction are critical drivers of cooperative behavior diffusion in networked settings. However, while these studies typically consider single-layer networks, our two-layer structure captures the distinct roles of upstream manufacturers and downstream service providers. This design offers a more nuanced representation of vertical industrial chain relationships.

Second, regarding thematic extension. Although existing UAV industry research has produced significant insights, it has predominantly focused on airspace management policy, regulatory frameworks, infrastructure planning [23, 24], and technological R&D in flight control systems, autonomous navigation, and sensor integration [25–27]. Limited studies have examined safety risk assessment and airworthiness certification [28, 29]. However, the micro-decision-making mechanisms underlying collaborative innovation between UAV manufacturers and service providers have received insufficient attention. Our study directly addresses this gap by modeling the strategic interactions between these two types of agents under bounded rationality and networked conditions. This extension effectively complements existing macro-level and technology-focused UAV research.

Third, regarding theoretical alignment. Our finding that the collaborative system may converge to either full collaboration or no collaboration depending on initial conditions echoes the path dependence phenomenon documented in innovation diffusion literature [46]. The positive role of cooperation trust aligns with the relational view of Dyer and Singh [50], which posits trust as a key source of interorganizational competitive advantage. The threshold effect of policy incentives we observe, where incentives below a critical level fail to trigger collaboration, is consistent with findings in green technology diffusion [51], suggesting that policy interventions must reach a minimum intensity to overcome coordination failures. While Tao [36] found that network structure alone significantly determines cooperation levels in smart grid networks, our results suggest that in the UAV industrial chain, the interplay between network structure and enterprise capability parameters, including technological accumulation, absorptive capacity, and cooperation trust, jointly determines the evolutionary outcome. This divergence likely reflects the distinctive characteristics of the UAV industry, where technological complexity and cross-scenario diversity create stronger interdependencies between upstream and downstream actors than in more standardized industrial contexts.

6.3 Policy and management recommendations

In order to promote collaborative innovation in the UAV industrial chain and accelerate the development of the low-altitude economy, the following recommendations are proposed from both governmental and industrial perspectives:

At the level of government policy design, it is imperative to enhance top-level design and implement targeted incentives to establish a conducive environment for collaborative innovation. We recommend that the government formulate customized policies regarding R&D subsidies, tax incentives, and application demonstration support. To this end, the government should takes into account the maturity of UAV technology and the characteristics of the various application scenarios. In the context of nascent industrialization, where the risks associated with collaborative innovation are pronounced, it is imperative to furnish projects with robust initial support to mitigate the financial burden imposed by trial and error expenses for enterprises. Concurrently, a reasonable cost-sharing and risk compensation mechanism for collaborative innovation should be established. Drawing on experiences from other industries, we propose methods such as the establishment of an industrial chain collaborative innovation fund. The purpose of such a fund would be to provide moderate compensation for the additional costs and innovation risks borne by manufacturers and service providers during collaboration. Support should be allocated to small and medium-sized service providers in a way that enhances their willingness and capacity to participate [52].

In order to consolidate their technological foundations, it is incumbent upon UAV manufacturers operating at the industrial and enterprise level to invest continuously in R&D of core technologies. It is incumbent upon service providers to pursue ongoing enhancement of their industry-specific application knowledge, with a view to bolstering their capabilities in technology integration and scenario-based innovation. Both parties can enhance their knowledge absorption and transformation capabilities, as well as their mutual trust. This can be achieved through various approaches, including the establishment of joint R&D centers and the organization of regular exchanges [53]. In addition, a collaborative governance and benefit-sharing mechanism based on long-term value should be constructed. The preliminary stage of the process is to clarify three matters. Firstly, the intellectual property ownership must be clarified. Secondly, the benefit distribution ratios must be clarified. Thirdly, the liability for breach of contract must be clarified. Trusted technologies such as blockchain can facilitate the traceability of the cooperation process and the establishment of information transparency. Institutionalized measures have been shown to reduce the risks associated with cooperation, whilst concomitantly enhancing the level of trust amongst participants and contributing to the stabilization of expectations regarding future cooperation.

6.4 Research outlook

This study preliminarily explores the dynamic mechanisms of collaborative innovation in the UAV industrial chain by constructing a network evolutionary game model. However, this study has several limitations that suggest avenues for future research. First, the model parameters are primarily based on typical values. Future research could calibrate and validate the model using more realistic data obtained through enterprise surveys and case analysis. Second, the network scale comprises 50 manufacturer nodes and 150 service provider nodes. While this captures the essential structural features of the UAV industrial chain, scale-free network properties manifest most reliably at larger scales. Future research could extend the network scale using computational approaches or employ ensemble simulations across multiple network realizations to mitigate finite-size effects. Third, the paper considers two types of agents: manufacturers and service providers. The incorporation of a more diverse range of agents, including government entities and academic institutions, could be a future avenue for model extension. Fourth, the current model assumes that manufacturers and service providers operate within the same institutional and regulatory framework. In reality, manufacturers are often concentrated in specific countries while service providers may operate across multiple regulatory regions. Future research could introduce parameters such as regulatory compatibility and cross-border costs to enhance the model applicability to the global UAV industrial chain. Further targeted case studies and simulation analyses are recommended. To this end, specific industry scenarios should be considered, such as urban logistics UAVs or power inspection UAVs. This would make the findings more practically valuable.

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Footnotes

Edited by: Juan Carlos Nuño, Polytechnic University of Madrid, Spain

Reviewed by: David Conchouso Gonzalez, Monterrey Institute of Technology and Higher Education (ITESM), Mexico

Meng Xiao, Shenyang University of Technology, China